A120733 -id:A120733 - cp's OEIS frontend

A321515 Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows and columns.

1, 1, 3, 19, 137, 1209, 12899, 160395, 2276229, 36323217, 643848837, 12551081501, 266868756473, 6146455542737, 152439235077709, 4050427673024753, 114791270281213209, 3456412742412516649, 110191808168628510207, 3708004806262196242699, 131339701217968663631857

Offset: 0

Gus Wiseman, Nov 13 2018

nonn

			The a(3) = 19 matrices:
  [3] [2 1] [1 2]
.
  [2] [2 0] [1 1] [1 1] [1] [1 0] [1 0] [0 2] [0 1] [0 1]
  [1] [0 1] [1 0] [0 1] [2] [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]

Andrew Howroyd, Table of n, a(n) for n = 0..40

Cf. A007716, A120733, A283877, A316980, A319559, A321446, A321586, A321588.

multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
Table[Length[Select[multsubs[Tuples[Range[n],2],n],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@prs2mat[#],UnsameQ@@Transpose[prs2mat[#]]]&]],{n,5}]

\\ Q(m,n,wf) defined in A321588.
seq(n)={my(R=vectorv(n,m,Q(m,n,w->1/(1 - y^w) + O(y*y^n)))); for(i=2, #R, R[i] -= i*R[i-1]); Vec(1 + vecsum(vecsum(R)))} \\ Andrew Howroyd, Jan 24 2024

a(7) onwards from Andrew Howroyd, Jan 20 2024

A321585 Number of connected nonnegative integer matrices with sum of entries equal to n and no zero rows or columns.

Original entry on oeis.org

1, 1, 3, 11, 52, 312, 2290, 19920, 200522, 2293677, 29389005, 416998371, 6490825772, 109972169413, 2014696874717, 39684502845893, 836348775861331, 18777970539419957, 447471215460930665, 11279275874429302811, 299844572529989373703, 8383794111721619471384, 245956060268568277412668

Offset: 0

Gus Wiseman, Nov 13 2018

nonn

A matrix is connected if the positions in each row (or each column) of the nonzero entries form a connected hypergraph.

			The a(3) = 11 matrices:
  [3] [2 1] [1 2] [1 1 1]
.
  [2] [1 1] [1 1] [1] [1 0] [0 1]
  [1] [1 0] [0 1] [2] [1 1] [1 1]
.
  [1]
  [1]
  [1]

Andrew Howroyd, Table of n, a(n) for n = 0..100

Cf. A007718, A056156, A120733, A319557, A319565, A319647, A319616-A319629, A321584.

multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[multsubs[Tuples[Range[n],2],n],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],Length[csm[Map[Last,GatherBy[#,First],{2}]]]==1]&]],{n,5}] (* Mathematica 7.0+ *)

NonZeroCols(M)={my(C=Vec(M)); Mat(vector(#C, n,  sum(k=1, n, (-1)^(n-k)*binomial(n,k)*C[k])))}
ConnectedMats(M)={my([m,n]=matsize(M), R=matrix(m,n)); for(m=1, m, for(n=1, n, R[m,n] = M[m,n] - sum(i=1, m-1, sum(j=1, n-1, binomial(m-1,i-1)*binomial(n,j)*R[i,j]*M[m-i,n-j])))); R}
seq(n)={my(M=matrix(n,n,i,j,sum(k=1, n, binomial(i*j+k-1,k)*x^k, O(x*x^n) ))); Vec(1 + vecsum(vecsum(Vec( ConnectedMats( NonZeroCols( NonZeroCols(M)~))))))} \\ Andrew Howroyd, Jan 17 2024

a(7) onwards from Andrew Howroyd, Jan 17 2024

A321587 Number of (0,1)-matrices with n ones, no zero rows or columns, and distinct rows.

Original entry on oeis.org

1, 1, 3, 17, 129, 1227, 14123, 190265, 2934359, 50975647, 984801759, 20941104299, 486007744671, 12223797601887, 331190083773701, 9616356919931711, 297887922137531747, 9805965265937326129, 341827167387114704421, 12579123760272833723975, 487315396984696657840761

Offset: 0

Gus Wiseman, Nov 13 2018

nonn

Also number of colored compositions of n using all colors of an initial interval of the color palette such that all parts have different color patterns and the patterns for parts i have i distinct colors in increasing order. a(3) = 17: 2ab1a, 2ab1b, 1a2ab, 1b2ab, 3abc, 2ab1c, 2ac1b, 2bc1a, 1a2bc, 1b2ac, 1c2ab, 1a1b1c, 1a1c1b, 1b1a1c, 1b1c1a, 1c1a1b, 1c1b1a. - Alois P. Heinz, Sep 17 2019

			The a(3) = 17 matrices:
  [1 1 1]
.
  [1 1] [1 1] [1 1 0] [1 0 1] [1 0] [1 0 0] [0 1 1] [0 1] [0 1 0] [0 0 1]
  [1 0] [0 1] [0 0 1] [0 1 0] [1 1] [0 1 1] [1 0 0] [1 1] [1 0 1] [1 1 0]
.
  [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]

Alois P. Heinz, Table of n, a(n) for n = 0..200

Cf. A007716, A049311, A101370, A120733, A283877, A316980, A321446, A321515.

Row sums of A327583, A327584.

C:= binomial:
b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
      b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k, i), j), j=0..n/i)))
    end:
a:= n-> add(add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
seq(a(n), n=0..21);  # Alois P. Heinz, Sep 16 2019

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@prs2mat[#]]&]],{n,5}]

a(n) ~ c * d^n * n!, where d = 1.938593839617140963759657977... and c = 0.350862127201784401195038... - Vaclav Kotesovec, Feb 05 2022

a(7)-a(20) from Alois P. Heinz, Sep 16 2019

A321662 Number of non-isomorphic multiset partitions of weight n whose incidence matrix has all distinct entries.

Original entry on oeis.org

1, 1, 1, 3, 3, 5, 13, 15, 23, 33, 49, 59, 83, 101, 133, 281, 321, 477, 655, 941, 1249, 1795, 2241, 3039, 3867, 5047, 6257, 8063, 11459, 13891, 18165, 23149, 29975, 37885, 49197, 61829, 89877, 109165, 145673, 185671, 246131, 310325, 408799, 514485, 668017, 871383

Offset: 0

Gus Wiseman, Nov 15 2018

nonn

The incidence matrix of a multiset partition has entry (i, j) equal to the multiplicity of vertex i in part j.
Also the number of positive integer matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with all different entries.
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

			Non-isomorphic representatives of the a(3) = 3 through a(7) = 15 multiset partitions:
  {{111}}    {{1111}}    {{11111}}    {{111111}}      {{1111111}}
  {{122}}    {{1222}}    {{11222}}    {{112222}}      {{1112222}}
  {{1}{11}}  {{1}{111}}  {{12222}}    {{122222}}      {{1122222}}
                         {{1}{1111}}  {{122333}}      {{1222222}}
                         {{11}{111}}  {{1}{11111}}    {{1223333}}
                                      {{11}{1111}}    {{1}{111111}}
                                      {{1}{11222}}    {{11}{11111}}
                                      {{11}{1222}}    {{111}{1111}}
                                      {{112}{222}}    {{1}{112222}}
                                      {{122}{222}}    {{11}{12222}}
                                      {{2}{11222}}    {{112}{2222}}
                                      {{22}{1222}}    {{122}{2222}}
                                      {{1}{11}{111}}  {{2}{112222}}
                                                      {{22}{12222}}
                                                      {{1}{11}{1111}}

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Cf. A000219, A007716, A008289, A059201, A114736, A117433, A120733, A121860, A321653, A321659, A321660, A321661.

(* b = A121860 *) b[n_] := Sum[n!/(d! (n/d)!), {d, Divisors[n]}];
(* c = A008289 *) c[n_, k_] := c[n, k] = If[n < k || k < 1, 0, If[n == 1, 1, c[n - k, k] + c[n - k, k - 1]]];
a[n_] := If[n == 0, 1, Sum[ (b[k] + b[k + 1] - 2) c[n, k], {k, 1, n}]];
a /@ Range[0, 45] (* Jean-François Alcover, Sep 14 2019 *)

\\ here b(n) is A121860(n).
b(n)={sumdiv(n, d, n!/(d!*(n/d)!))}
seq(n)={my(B=vector((sqrtint(8*(n+1))+1)\2, n, if(n==1, 1, b(n-1)+b(n)-2))); apply(p->sum(i=0, poldegree(p), B[i+1]*polcoef(p, i)), Vec(prod(k=1, n, 1 + x^k*y + O(x*x^n))))} \\ Andrew Howroyd, Nov 16 2018

a(n) = Sum_{k>=1} (A121860(k) + A121860(k+1) - 2)*A008289(n,k) for n > 0. - Andrew Howroyd, Nov 17 2018

Terms a(11) and beyond from Andrew Howroyd, Nov 16 2018

A323302 Number of ways to arrange the parts of the integer partition with Heinz number n into a matrix with equal row-sums and equal column-sums.

Original entry on oeis.org

1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 0, 3, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 4, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 0, 1, 0, 0, 0, 0

Offset: 1

Gus Wiseman, Jan 13 2019

nonn

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

			The a(900) = 12 matrix-arrangements of (3,3,2,2,1,1):
  [1 2 3] [1 3 2] [2 1 3] [2 3 1] [3 1 2] [3 2 1]
  [3 2 1] [3 1 2] [2 3 1] [2 1 3] [1 3 2] [1 2 3]
.
  [1 3] [1 3] [2 2] [2 2] [3 1] [3 1]
  [2 2] [3 1] [1 3] [3 1] [1 3] [2 2]
  [3 1] [2 2] [3 1] [1 3] [2 2] [1 3]

Positions of zeros are a superset of A106543.
Cf. A000005, A001222, A006052, A007016, A008480, A056239, A112798, A120733, A319056, A321719, A321721.
Cf. A323300, A323303, A323305, A323306, A323347, A323349.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS,facs[n],{2}]),SameQ@@Length/@#&];
Table[Length[Select[ptnmats[n],And[SameQ@@Total/@#,SameQ@@Total/@Transpose[#]]&]],{n,100}]

A321411 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 0, 4, 6, 16, 25

Offset: 0

Gus Wiseman, Nov 16 2018

A multiset is aperiodic if its multiplicities are relatively prime.
Also the number of nonnegative integer symmetric matrices up to row and column permutations with sum of elements equal to n and no zero rows or columns, with relatively prime row sums (or column sums) and no row or column having a common divisor > 1 or summing to 1.
The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

			Non-isomorphic representatives of the a(5) = 1 through a(9) = 16 multiset partitions:
  {{12}{122}}  {{112}{1222}}    {{112}{12222}}    {{1112}{11222}}
               {{12}{12222}}    {{122}{11222}}    {{1112}{12222}}
               {{12}{13}{233}}  {{12}{123}{233}}  {{12}{1222222}}
               {{13}{23}{123}}  {{13}{112}{233}}  {{12}{123}{2333}}
                                {{13}{122}{233}}  {{12}{13}{23333}}
                                {{23}{123}{123}}  {{12}{223}{1233}}
                                                  {{13}{112}{2333}}
                                                  {{13}{223}{1233}}
                                                  {{13}{23}{12333}}
                                                  {{23}{122}{1233}}
                                                  {{23}{123}{1233}}
                                                  {{12}{12}{34}{234}}
                                                  {{12}{12}{34}{344}}
                                                  {{12}{13}{14}{234}}
                                                  {{12}{13}{24}{344}}
                                                  {{12}{14}{34}{234}}

Cf. A000219, A007716, A120733, A138178, A302545, A316983, A319616.

Cf. A320796, A320797, A320803, A320806, A320809, A320813, A321283, A321408-A321413.

A321586 Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows (or distinct columns).

Original entry on oeis.org

1, 1, 4, 26, 204, 1992, 23336, 318080, 4948552, 86550424, 1681106080, 35904872576, 836339613984, 21100105791936, 573194015723840, 16681174764033728, 517768654898701120, 17074080118403865856, 596117945858272441408, 21967609729338776864384, 852095613819396775627200

Offset: 0

Gus Wiseman, Nov 13 2018

nonn

			The a(3) = 26 matrices:
  [3][21][12][111]
.
  [2][20][11][11][110][101][1][10][10][100][02][011][01][01][010][001]
  [1][01][10][01][001][010][2][11][02][011][10][100][20][11][101][110]
.
  [100][100][010][010][001][001]
  [010][001][100][001][100][010]
  [001][010][001][100][010][100]

Alois P. Heinz, Table of n, a(n) for n = 0..200

Cf. A007716, A049311, A101370, A120733, A283877, A316980, A321446, A321587.

Row sums of A327245.

C:= binomial:
b:= proc(n, i, k, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
      b(n-i*j, min(n-i*j, i-1), k, p+j)*C(C(k+i-1, i), j), j=0..n/i)))
    end:
a:= n-> add(add(b(n$2, i, 0)*(-1)^(k-i)*C(k, i), i=0..k), k=0..n):
seq(a(n), n=0..21);  # Alois P. Heinz, Sep 16 2019

multsubs[set_,k_]:=If[k==0,{{}},Join@@Table[Prepend[#,set[[i]]]&/@multsubs[Drop[set,i-1],k-1],{i,Length[set]}]];
prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
Table[Length[Select[multsubs[Tuples[Range[n],2],n],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@prs2mat[#]]&]],{n,5}]

a(7)-a(20) from Alois P. Heinz, Sep 16 2019

A321646 Number of distinct row/column permutations of Ferrers diagrams of integer partitions of n.

Original entry on oeis.org

1, 1, 2, 6, 15, 39, 108, 290, 781, 2050, 5434, 14210, 37150, 96347, 248250, 636278, 1620721, 4108340, 10361338, 26016060, 65019655, 161831393, 401090324, 990229108, 2435316984, 5967684036, 14572351628, 35464928382, 86033632280, 208062026930, 501676936146

Offset: 0

Gus Wiseman, Nov 15 2018

nonn

			The a(4) = 15 diagrams:
  o o o o
.
  o o o   o o o   o o o   o o   o         o         o
  o         o         o   o o   o o o   o o o   o o o
.
  o o   o o   o     o       o     o
  o       o   o o   o     o o     o
  o       o   o     o o     o   o o
.
  o
  o
  o
  o

Cf. A000219, A008480, A049311, A068313, A101370, A120733, A122111, A321645, A321647, A321648, A321655.

conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
Table[Sum[Length[Permutations[y]]*Length[Permutations[conj[y]]],{y,IntegerPartitions[n]}],{n,10}]

a(n) = Sum_{k = 1..A000041(n)} A008480(A215366(n,k)) * A008480(A122111(A215366(n,k))).

a(11)-a(30) from Alois P. Heinz, Nov 15 2018

A321654 Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, with distinct row sums and distinct column sums.

Original entry on oeis.org

1, 1, 1, 13, 13, 45, 681, 885, 2805, 8301, 237213

Offset: 0

Gus Wiseman, Nov 15 2018

			The a(3) = 13 matrices:
  [3] [2 1] [1 2]
.
  [2] [2 0] [1 1] [1 1] [1] [1 0] [1 0] [0 2] [0 1] [0 1]
  [1] [0 1] [1 0] [0 1] [2] [1 1] [0 2] [1 0] [2 0] [1 1]

Cf. A000219, A001970, A007716, A068313, A114736, A117433, A120733, A319646, A321645, A321646, A321652.

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
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],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@Total/@prs2mat[#],UnsameQ@@Total/@Transpose[prs2mat[#]]]&]],{n,5}]

A321659 Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, whose nonzero entries are all distinct.

Original entry on oeis.org

1, 1, 1, 9, 9, 17, 161, 169, 313, 465, 5313, 5465, 10457, 15313, 25009, 271929, 286329, 537953, 799121, 1297369, 1805161, 20532897, 21292017, 40508297, 59738825, 97431073, 135137569, 209525865, 2089381929, 2200470833, 4135252289, 6124698121, 9937836505

Offset: 0

Gus Wiseman, Nov 15 2018

nonn

			The a(5) = 17 matrices:
  [5] [4 1] [3 2] [2 3] [1 4]
.
  [4] [4 0] [3] [3 0] [2] [2 0] [1] [1 0] [0 4] [0 3] [0 2] [0 1]
  [1] [0 1] [2] [0 2] [3] [0 3] [4] [0 4] [1 0] [2 0] [3 0] [4 0]

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Cf. A000219, A007716, A008289, A101370, A114736, A117433, A120733, A321645, A321653, A321655, A321660, A321661, A321662.

prs2mat[prs_]:=Table[Count[prs,{i,j}],{i,Union[First/@prs]},{j,Union[Last/@prs]}];
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],And[Union[First/@#]==Range[Max@@First/@#],Union[Last/@#]==Range[Max@@Last/@#],UnsameQ@@DeleteCases[Join@@prs2mat[#],0]]&]],{n,5}]

\\ here b(n) is A101370(n).
b(n)={sum(m=0, n, sum(k=0, m, stirling(m,k,2)*k!)^2*polcoef(log(1+x+O(x*x^n))^m, n)/m!)}
seq(n)={my(B=vector((sqrtint(8*(n+1))+1)\2, n, b(n-1))); apply(p->sum(i=0, poldegree(p), B[i+1]*i!*polcoef(p, i)), Vec(prod(k=1, n, 1 + x^k*y + O(x*x^n))))} \\ Andrew Howroyd, Nov 16 2018

a(n) = Sum_{k>=1} A101370(k)*k!*A008289(n,k) for n > 0. - Andrew Howroyd, Nov 17 2018

Terms a(11) and beyond from Andrew Howroyd, Nov 16 2018

cp's OEIS Frontend

A321515 Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows and columns.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A321585 Number of connected nonnegative integer matrices with sum of entries equal to n and no zero rows or columns.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A321587 Number of (0,1)-matrices with n ones, no zero rows or columns, and distinct rows.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A321662 Number of non-isomorphic multiset partitions of weight n whose incidence matrix has all distinct entries.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A323302 Number of ways to arrange the parts of the integer partition with Heinz number n into a matrix with equal row-sums and equal column-sums.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A321411 Number of non-isomorphic self-dual multiset partitions of weight n with no singletons, with aperiodic parts whose sizes are relatively prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

A321586 Number of nonnegative integer matrices with sum of entries equal to n, no zero rows or columns, and distinct rows (or distinct columns).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A321646 Number of distinct row/column permutations of Ferrers diagrams of integer partitions of n.

Views

Author