A048291 -id:A048291 - cp's OEIS frontend

A342796 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(6,n) (with n at least 4) missing three edges, where all three removed edges are incident to the same vertex in the 6-point set.

709682, 77784248, 6126191066, 427218509360, 28245026082242, 1821452259070568, 116065734824421866, 7353059854962677600, 464513906582191544402, 29303821259651224580888, 1847364138146506201033466, 116421875056692663153073040

Offset: 4

Roman I. Vasquez, Mar 24 2021

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to the same point in A. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 6 X n matrices (with n at least 4) with three fixed zero entries all in the same row and no zero rows or columns.
Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where all three removed edges are incident same vertex in A.

Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (120,-4593,69688,-428787,978768,-615195).

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

a(n) = 29791*63^(n-3) - 46666*31^(n-3) + 20305*15^(n-3) - 3700*7^(n-3) + 275*3^(n-3) - 5.

A342850 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 3-point set and none of the removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

162, 1242, 9018, 64098, 451602, 3169962, 22215978, 155590578, 1089370242, 7626300282, 53386227738, 373709971458, 2615988932082, 18311979920202, 128184031628298, 897288737958738, 6281022715393122, 43967163656797722, 307770159544721658

Offset: 4

Roman I. Vasquez, Mar 24 2021

Start with a complete bipartite graph K(3,n) with vertex sets A and B where |A| = 3 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries none of which are in the same row or column with no zero rows or columns.
Take a complete bipartite graph K(3,n) (with n at least 4) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing three edges, where all three removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (10,-21).

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

a(n) = 27*7^(n-3) - 3^(n-1).

G.f.: 54*x^4*(3 - 7*x)/(1 - 10*x + 21*x^2). - Stefano Spezia, Mar 25 2021

A343372 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 3-point set and exactly two removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

112, 922, 6880, 49450, 350032, 2461882, 17268160, 120982090, 847189552, 5931271642, 41521735840, 290660653930, 2034650086672, 14242627134202, 99698619521920, 697891025400970, 4885239244049392

Offset: 4

Steven Schlicker, Apr 12 2021

Start with a complete bipartite graph K(3,n) with vertex sets A and B where |A| = 3 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.
Take a complete bipartite graph K(3,n) (with n at least 4) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing three edges, where exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.

Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Drop[CoefficientList[Series[2 x^4*(56 - 155 x + 105 x^2)/(1 - 11 x + 31 x^2 - 21 x^3), {x, 0, 20}], x], 4] (* Michael De Vlieger, Apr 13 2021 *)
LinearRecurrence[{11,-31,21},{112,922,6880},20] (* Harvey P. Dale, Apr 06 2025 *)

a(n) = 3*7^(n-2) - 4*3^(n-2) + 1.

G.f.: 2*x^4*(56 - 155*x + 105*x^2)/(1 - 11*x + 31*x^2 - 21*x^3). - Stefano Spezia, Apr 13 2021

A343374 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(5,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 5-point set and exactly two removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

58984, 2445394, 86336272, 2843754442, 90733504504, 2851869796354, 88998264600352, 2767824089452282, 85935878802252424, 2666013369738472114, 82676439390965238832, 2563420051241406849322, 79472778433612932113944, 2463757486872117920024674, 76378002443759735050203712

Offset: 4

Steven Schlicker, Apr 12 2021

Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 5 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.
Take a complete bipartite graph K(5,n) (with n at least 4) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,n) graph after removing three edges, where exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.

Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (57,-1002,6562,-15381,9765).

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

a(n) = 105*31^(n-2) - 217*15^(n-2) + 148*7^(n-2) - 13*3^(n-1) + 3.

G.f.: 2*x^4*(29492 - 458347*x + 3025391*x^2 - 7090641*x^3 + 4501665*x^4)/((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 15*x)*(1 - 31*x)). - Stefano Spezia, Sep 01 2025

Typo in a(14) corrected by Georg Fischer, Dec 08 2021

A343800 Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(6,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 6-point set and exactly two removed edges are incident to the same vertex in the other set.

Original entry on oeis.org

978064, 86336272, 6348047008, 430432446400, 28099268578864, 1801251897183472, 114448204851788608, 7240412761411376800, 457083355837815526864, 28825337854868779198672, 1816898392511988031818208, 114492570488330137017059200, 7213899161676798784740778864

Offset: 4

Rachel Wofford, Apr 29 2021

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.
Number of {0,1} 6 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.
Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.

Steven Schlicker, Roman Vasquez, and Rachel Wofford, Integer Sequences from Configurations in the Hausdorff Metric Geometry via Edge Covers of Bipartite Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.6.6.
Index entries for linear recurrences with constant coefficients, signature (120,-4593,69688,-428787,978768,-615195).

Sequences of segments from removing edges from bipartite graphs A335608-A335613, A337416-A337418, A340173-A340175, A340199-A340201, A340897-A340899, A342580, A342796, A342850, A340403-A340405, A340433-A340438, A341551-A341553, A342327-A342328, A343372-A343374, A343800. Polygonal chain sequences A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934, A152939. Number of {0,1} n X n matrices with no zero rows or columns A048291.

Array[465*63^# - 1110*31^# + 967*15^# - 388*7^# + 70*3^# - 4 &[# - 2] &, 12, 4] (* Michael De Vlieger, May 01 2021 *)

a(n) = 465*63^(n-2) - 1110*31^(n-2) + 967*15^(n-2) - 388*7^(n-2) + 70*3^(n-2) - 4.

A120732 Number of square matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n.

Original entry on oeis.org

1, 1, 3, 15, 107, 991, 11267, 151721, 2360375, 41650861, 821881709, 17932031225, 428630422697, 11138928977049, 312680873171465, 9428701154866535, 303957777464447449, 10431949496859168189, 379755239311735494421

Offset: 0

Vladeta Jovovic, Aug 18 2006

nonn

			From _Gus Wiseman_, Nov 14 2018: (Start)
The a(3) = 15 matrices:
  [3]
.
  [2 0] [1 1] [1 1] [1 0] [1 0] [0 2] [0 1] [0 1]
  [0 1] [1 0] [0 1] [1 1] [0 2] [1 0] [2 0] [1 1]
.
  [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
  [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
  [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
(End)

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A007716, A048291, A054976, A057149, A057150, A057151, A104601, A104602, A120733, A138178, A316983, A319616.

Table[1/n!*Sum[(-1)^(n-k)*StirlingS1[n,k]*Sum[(m!)^2*StirlingS2[k,m]^2,{m,0,k}],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, May 07 2014 *)
multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]]; Table[Length[Select[multsubs[Tuples[Range[n],2],n],Union[First/@#]==Union[Last/@#]==Range[Max@@First/@#]&]],{n,5}] (* Gus Wiseman, Nov 14 2018 *)

a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)*A048144(k).
G.f.: Sum_{n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*((1-x)^(-j)-1)^n.
a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.4670932578797312973586879293426... . - Vaclav Kotesovec, May 07 2014
In closed form, c = 2^(log(2)/2-2) / (log(2) * sqrt(Pi*(1-log(2)))). - Vaclav Kotesovec, May 03 2015
G.f.: Sum_{n>=0} (1-x)^n * (1 - (1-x)^n)^n. - Paul D. Hanna, Mar 26 2018

A055601 Number of n X n binary matrices with no zero rows.

Original entry on oeis.org

1, 1, 9, 343, 50625, 28629151, 62523502209, 532875860165503, 17878103347812890625, 2375680873491867011912191, 1255325460068093790930770843649, 2644211984585174742731315532085090303, 22235498641774645581443610453175918212890625

Offset: 0

Vladeta Jovovic, Jun 01 2000

More generally, Sum_{n>=0} m^n * q^(n^2) * exp(b*q^n*x) * x^n / n! = Sum_{n>=0} (m*q^n + b)^n * x^n / n! for all q, m, b. - Paul D. Hanna, Jan 02 2008

			A(x) = 1 + x + 3^2*x^2/2! + 7^3*x^3/3! + 15^4*x^4/4! +... + (2^n-1)^n*x^n/n! +...
A(x) = exp(-x) + 2*exp(-2x) + 2^4*exp(-4x)*x^2/2! + 2^9*exp(-8x)*x^3/3! +...+ 2^(n^2)*exp(-2^n*x)*x^n/n! +...
This is a special case of the more general statement: Sum_{n>=0} m^n * F(q^n*x)^b * log( F(q^n*x) )^n / n! = Sum_{n>=0} x^n * [y^n] F(y)^(m*q^n + b) where F(x) = exp(x), q=2, m=1, b=-1. - _Paul D. Hanna_, Jan 02 2008

Kenny Lau, Table of n, a(n) for n = 0..57

Cf. A048291, A092477, A136516, A303560.

a:= n-> mul(Stirling2(n+1, 2), j=1..n): seq(a(n), n=0..10); # Zerinvary Lajos, Jan 01 2009

Join[{1},Table[(2^n-1)^n,{n,16}]] (* Vladimir Joseph Stephan Orlovsky, Feb 14 2011 *)

a(n)=n!*polcoeff(sum(k=0,n,2^(k^2)*exp(-2^k*x)*x^k/k!),n) \\ Paul D. Hanna, Jan 02 2008

a = lambda n:((1<Kenny Lau, Jul 05 2016

N = 58
base = 0
a = []
for i in range(N):
    a += [base**i]
    base = (base<<1)|1 #base = base*2+1
print(a)
# Kenny Lau, Jul 05 2016

a(n) = A092477(n, n) for n>0.
a(n) = (2^n - 1 )^n. - Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
a(n) = Sum_{k=0..n} (-1)^k*C(n, k)*2^((n-k)*n).
E.g.f.: A(x) = Sum_{n>=0} 2^(n^2) * exp(-2^n*x) * x^n/n!. - Paul D. Hanna, Jan 02 2008
O.g.f.: Sum_{n>=0} 2^(n^2)*x^n/(1 + 2^n*x)^(n+1). - Paul D. Hanna, Jan 20 2010
Sum_{n>=1} 1/a(n) = A303560. - Amiram Eldar, Nov 18 2020

A104602 Number of square (0,1)-matrices with exactly n entries equal to 1 and no zero row or columns.

Original entry on oeis.org

1, 1, 2, 10, 70, 642, 7246, 97052, 1503700, 26448872, 520556146, 11333475922, 270422904986, 7016943483450, 196717253145470, 5925211960335162, 190825629733950454, 6543503207678564364, 238019066600097607402, 9153956822981328930170, 371126108428565106918404

Offset: 0

Ralf Stephan, Mar 27 2005

nonn

Number of square (0,1)-matrices with exactly n entries equal to 1 and no zero row or columns, up to row and column permutation, is A057151(n). - Vladeta Jovovic, Mar 25 2006

			From _Gus Wiseman_, Nov 14 2018: (Start)
The a(3) = 10 matrices:
  [1 1] [1 1] [1 0] [0 1]
  [1 0] [0 1] [1 1] [1 1]
.
  [1 0 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] [0 0 1]
  [0 1 0] [0 0 1] [1 0 0] [0 0 1] [1 0 0] [0 1 0]
  [0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] [1 0 0]
(End)

Alois P. Heinz, Table of n, a(n) for n = 0..400
H. Cheballah, S. Giraudo, R. Maurice, Combinatorial Hopf algebra structure on packed square matrices, arXiv preprint arXiv:1306.6605 [math.CO], 2013-2015.
M. Maia and M. Mendez, On the arithmetic product of combinatorial species, arXiv:math/0503436 [math.CO], 2005.

Row sums of triangle A104601.

Cf. A048291, A049311, A054976, A057150, A057151, A101370, A120732, A120733, A138178, A316983, A319616.

Table[1/n!*Sum[StirlingS1[n,k]*Sum[(m!)^2*StirlingS2[k, m]^2, {m, 0, k}],{k,0,n}],{n,1,20}] (* Vaclav Kotesovec, May 07 2014 *)
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],Union[First/@#]==Union[Last/@#]==Range[Max@@First/@#]&]],{n,5}] (* Gus Wiseman, Nov 14 2018 *)

a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A048144(k). - Vladeta Jovovic, Mar 25 2006
G.f.: Sum_{n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*((1+x)^j-1)^n. - Vladeta Jovovic, Mar 25 2006
a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.28889864564457451375789435201798... . - Vaclav Kotesovec, May 07 2014
In closed form, c = 1 / (log(2) * 2^(log(2)/2+2) * sqrt(Pi*(1-log(2)))). - Vaclav Kotesovec, May 03 2015
G.f.: Sum_{n>=0} ((1+x)^n - 1)^n / (1+x)^(n*(n+1)). - Paul D. Hanna, Mar 26 2018

More terms from Vladeta Jovovic, Mar 25 2006

a(0)=1 prepended by Alois P. Heinz, Jan 14 2015

A054976 Number of binary n X n matrices with no zero rows or columns, up to row and column permutation.

Original entry on oeis.org

1, 3, 17, 179, 3835, 200082, 29610804, 13702979132, 20677458750966, 103609939177198046, 1745061194503344181714, 99860890306900024150675406, 19611238933283757244479826044874, 13340750149227624084760722122669739026, 31706433098827528779057124372265863803044450

Offset: 1

Vladeta Jovovic, May 27 2000

Also the number of non-isomorphic set multipartitions (multisets of sets) with n parts and n vertices. - Gus Wiseman, Nov 18 2018

			From _Gus Wiseman_, Nov 18 2018: (Start)
Inequivalent representatives of the a(3) = 17 matrices:
  100 100 100 100 100 010 010 001 001 001 001 110 101 101 011 011 111
  100 010 001 011 011 001 101 001 101 011 111 101 011 011 011 111 111
  011 001 011 011 111 111 011 111 011 111 111 011 011 111 111 111 111
Non-isomorphic representatives of the a(1) = 1 through a(3) = 17 set multipartitions:
  {{1}}  {{1},{2}}      {{1},{2},{3}}
         {{2},{1,2}}    {{1},{1},{2,3}}
         {{1,2},{1,2}}  {{1},{3},{2,3}}
                        {{1},{2,3},{2,3}}
                        {{2},{1,3},{2,3}}
                        {{2},{3},{1,2,3}}
                        {{3},{1,3},{2,3}}
                        {{3},{3},{1,2,3}}
                        {{1,2},{1,3},{2,3}}
                        {{1},{2,3},{1,2,3}}
                        {{1,3},{2,3},{2,3}}
                        {{3},{2,3},{1,2,3}}
                        {{1,3},{2,3},{1,2,3}}
                        {{2,3},{2,3},{1,2,3}}
                        {{3},{1,2,3},{1,2,3}}
                        {{2,3},{1,2,3},{1,2,3}}
                        {{1,2,3},{1,2,3},{1,2,3}}
(End)

Andrew Howroyd, Table of n, a(n) for n = 1..50

Column sums of A057150.

Cf. A007716, A048291 (labeled), A049311, A057149, A057151, A104601, A104602, A319616, A320808.

A002724 = Cases[Import["https://oeis.org/A002724/b002724.txt", "Table"], {, }][[All, 2]];
A002725 = Cases[Import["https://oeis.org/A002725/b002725.txt", "Table"], {, }][[All, 2]];
a[n_] := A002724[[n + 1]] - 2 A002725[[n]] + A002724[[n]];
a /@ Range[1, 13] (* Jean-François Alcover, Sep 14 2019 *)

a(n) = A002724(n) - 2*A002725(n-1) + A002724(n-1).

More terms from David Wasserman, Mar 06 2002

Terms a(14) and beyond from Andrew Howroyd, Apr 11 2020

A094000 Number of n X n (0,1)-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.

Original entry on oeis.org

1, 1, 3, 29, 1015, 126651, 53354350, 74698954306, 350688201987402, 5624061753186933530, 314512139441575825493524, 62498777166571927258267336860, 44831219113504221199415663547412096

Offset: 0

Goran Kilibarda and Vladeta Jovovic, May 30 2004

Main diagonal of A059202.

G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in

G. C. Greubel, Table of n, a(n) for n = 0..59
Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.

Cf. A048291, A059202, A088309.

Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763

f[n_] := Sum[ StirlingS1[n + 1, k] Binomial[2^(k - 1) - 1, n], {k, 0, n + 1}]; Table[ f[n], {n, 0, 12}] (* Robert G. Wilson v, Jun 01 2004 *)

a(n) = sum(k=0, n+1, stirling(n+1, k, 1)*binomial(2^(k-1)-1, n)); \\ Michel Marcus, Dec 17 2022

a(n) = Sum_{k=0..n+1} Stirling1(n+1, k)*binomial(2^(k-1)-1, n).

a(n) ~ binomial(2^n,n). - Vaclav Kotesovec, Mar 18 2014

More terms from Robert G. Wilson v, Jun 01 2004

cp's OEIS Frontend

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A054976 Number of binary n X n matrices with no zero rows or columns, up to row and column permutation.