A319616 -id:A319616 - cp's OEIS frontend

A340600 Number of non-isomorphic balanced multiset partitions of weight n.

1, 1, 0, 4, 7, 16, 52, 206, 444, 1624, 5462, 19188, 62890, 215367, 765694, 2854202, 10634247, 39842786, 150669765, 581189458, 2287298588, 9157598354, 37109364812, 151970862472, 629048449881, 2635589433705, 11184718653563, 48064965080106, 208988724514022, 918639253237646, 4079974951494828

Offset: 0

Gus Wiseman, Feb 05 2021

nonn

We define a multiset partition to be balanced if it has exactly as many parts as the greatest size of a part.

			Non-isomorphic representatives of the a(1) = 1 through a(5) = 16 multiset partitions (empty column indicated by dot):
  {{1}}  .  {{1},{1,1}}  {{1,1},{1,1}}  {{1},{1},{1,1,1}}
            {{1},{2,2}}  {{1,1},{2,2}}  {{1},{1},{1,2,2}}
            {{1},{2,3}}  {{1,2},{1,2}}  {{1},{1},{2,2,2}}
            {{2},{1,2}}  {{1,2},{2,2}}  {{1},{1},{2,3,3}}
                         {{1,2},{3,3}}  {{1},{1},{2,3,4}}
                         {{1,2},{3,4}}  {{1},{2},{1,2,2}}
                         {{1,3},{2,3}}  {{1},{2},{2,2,2}}
                                        {{1},{2},{2,3,3}}
                                        {{1},{2},{3,3,3}}
                                        {{1},{2},{3,4,4}}
                                        {{1},{2},{3,4,5}}
                                        {{1},{3},{2,3,3}}
                                        {{1},{4},{2,3,4}}
                                        {{2},{2},{1,2,2}}
                                        {{2},{3},{1,2,3}}
                                        {{3},{3},{1,2,3}}

The version for partitions is A047993.
The co-balanced version is A319616.
The cross-balanced version is A340651.
The twice-balanced version is A340652.
The version for factorizations is A340653.
A007716 counts non-isomorphic multiset partitions.
A007718 counts non-isomorphic connected multiset partitions.
A316980 counts non-isomorphic strict multiset partitions.
Other balance-related sequences:
- A098124 counts balanced compositions.
- A106529 lists balanced numbers.
- A340596 counts co-balanced factorizations.
- A340597 lists numbers with an alt-balanced factorization.
- A340598 counts balanced set partitions.
- A340599 counts alt-balanced factorizations.
Cf. A001055, A006141, A007717, A316983, A320663, A324522, A340654, A340655.

\\ See A340652 for G.
seq(n)={Vec(1 + sum(k=1,n,polcoef(G(n,n,k,y),k,y) - polcoef(G(n,n,k-1,y),k,y)))} \\ Andrew Howroyd, Jan 15 2024

a(11) onwards from Andrew Howroyd, Jan 15 2024

A057150 Triangle read by rows: T(n,k) = number of k X k binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 5, 2, 1, 0, 0, 4, 11, 2, 1, 0, 0, 3, 21, 14, 2, 1, 0, 0, 1, 34, 49, 15, 2, 1, 0, 0, 1, 33, 131, 69, 15, 2, 1, 0, 0, 0, 33, 248, 288, 79, 15, 2, 1, 0, 0, 0, 19, 410, 840, 420, 82, 15, 2, 1, 0, 0, 0, 14, 531, 2144, 1744, 497, 83, 15, 2, 1

Offset: 1

Vladeta Jovovic, Aug 14 2000

Also the number of non-isomorphic set multipartitions (multisets of sets) of weight n with k parts and k vertices. - Gus Wiseman, Nov 14 2018

			[1], [0,1], [0,1,1], [0,1,2,1], [0,0,5,2,1], [0,0,4,11,2,1], ...;
There are 8 square binary matrices with 5 ones, with no zero rows or columns, up to row and column permutation: 5 of size 3 X 3:
[0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 1 0] [0 1 1] [0 1 1] [1 1 0]
[1 1 1] [1 1 1] [1 0 1] [1 1 0] [1 1 0]
2 of size 4 X 4:
[0 0 0 1] [0 0 0 1]
[0 0 0 1] [0 0 1 0]
[0 0 1 0] [0 1 0 0]
[1 1 0 0] [1 0 0 1]
and 1 of size 5 X 5:
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[1 0 0 0 0].
From _Gus Wiseman_, Nov 14 2018: (Start)
Triangle begins:
   1
   0   1
   0   1   1
   0   1   2   1
   0   0   5   2   1
   0   0   4  11   2   1
   0   0   3  21  14   2   1
   0   0   1  34  49  15   2   1
   0   0   1  33 131  69  15   2   1
   0   0   0  33 248 288  79  15   2   1
Non-isomorphic representatives of the multiset partitions counted in row 6 {0,0,4,11,2,1} are:
  {{12}{13}{23}}  {{1}{1}{1}{234}}  {{1}{2}{3}{3}{45}}  {{1}{2}{3}{4}{5}{6}}
  {{1}{23}{123}}  {{1}{1}{24}{34}}  {{1}{2}{3}{5}{45}}
  {{13}{23}{23}}  {{1}{1}{4}{234}}
  {{3}{23}{123}}  {{1}{2}{34}{34}}
                  {{1}{3}{24}{34}}
                  {{1}{3}{4}{234}}
                  {{1}{4}{24}{34}}
                  {{1}{4}{4}{234}}
                  {{2}{4}{12}{34}}
                  {{3}{4}{12}{34}}
                  {{4}{4}{12}{34}}
(End)

Row sums give A057151.
Cf. A049311, A056037, A056079, A056080, A057149, A057151, A057152.
Cf. A007716, A048291, A054976, A101370, A104601, A104602, A120732, A120733, A135588, A319616, A321609, A321615.

permcount[v_List] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
c[p_List, q_List, k_] := SeriesCoefficient[Product[Product[(1 + O[x]^(k + 1) + x^LCM[p[[i]], q[[j]]])^GCD[p[[i]], q[[j]]], {j, 1, Length[q]}], {i, 1, Length[p]}], {x, 0, k}];
M[m_, n_, k_] := M[m, n, k] = Module[{s = 0}, Do[Do[s += permcount[p]* permcount[q]*c[p, q, k], {q, IntegerPartitions[n]}], {p, IntegerPartitions[m]}]; s/(m!*n!)];
T[n_, k_] := M[k, k, n] - 2*M[k, k - 1, n] + M[k - 1, k - 1, n];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 10 2019, after Andrew Howroyd *)

\\ See A321609 for M.
T(n,k) = M(k,k,n) - 2*M(k,k-1,n) + M(k-1,k-1,n); \\ Andrew Howroyd, Nov 14 2018

Duplicate seventh row removed by Gus Wiseman, Nov 14 2018

A320328 Number of square multiset partitions of integer partitions of n.

Original entry on oeis.org

1, 1, 2, 3, 6, 11, 20, 36, 65, 117, 214, 382, 679

Offset: 0

Gus Wiseman, Oct 11 2018

A multiset partition is square if its length is equal to its number of distinct atoms.

			The a(1) = 1 through a(6) = 20 square partitions:
  {{1}}  {{2}}    {{3}}      {{4}}        {{5}}          {{6}}
         {{1,1}}  {{1,1,1}}  {{2,2}}      {{1},{4}}      {{3,3}}
                  {{1},{2}}  {{1},{3}}    {{2},{3}}      {{1},{5}}
                             {{1,1,1,1}}  {{1},{1,3}}    {{2,2,2}}
                             {{1},{1,2}}  {{1},{2,2}}    {{2},{4}}
                             {{2},{1,1}}  {{2},{1,2}}    {{1},{1,4}}
                                          {{3},{1,1}}    {{4},{1,1}}
                                          {{1,1,1,1,1}}  {{1},{1,1,3}}
                                          {{1},{1,1,2}}  {{1,1},{1,3}}
                                          {{1,1},{1,2}}  {{1},{1,2,2}}
                                          {{2},{1,1,1}}  {{1,1},{2,2}}
                                                         {{1,2},{1,2}}
                                                         {{1},{2},{3}}
                                                         {{2},{1,1,2}}
                                                         {{3},{1,1,1}}
                                                         {{1,1,1,1,1,1}}
                                                         {{1},{1,1,1,2}}
                                                         {{1,1},{1,1,2}}
                                                         {{1,2},{1,1,1}}
                                                         {{2},{1,1,1,1}}

Cf. A000219, A001970, A047968, A050342, A089259, A141268, A261049, A289501, A305551, A316983, A319066, A319312, A319616, A320330, A320331.

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
Table[Length[Select[Join@@mps/@IntegerPartitions[n],Length[#]==Length[Union@@#]&]],{n,8}]

A320808 Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 0, 1, 0, 2, 4, 0, 1, 5, 4, 0, 1, 5, 5, 5, 0, 0, 1, 0, 2, 4, 0, 2, 10, 8, 0, 1, 9, 13, 7, 0, 1, 5, 12, 9, 7, 0, 0, 1, 0, 3, 6, 0, 3, 16, 12, 0, 2, 24, 33, 16, 0, 1, 14, 36, 29, 12, 0, 1, 9, 23, 29

Offset: 1

Gus Wiseman, Nov 09 2018

			Tetrangle begins:
  1  0    0      0        0          0
     0 1  0 1    0 1      0 1        0 1
          0 1 2  0 1 2    0 2 4      0 2 4
                 0 1 2 3  0 1 5 4    0 2 10 8
                          0 1 5 5 5  0 1 9 13 7
                                     0 1 5 12 9 7

Triangle sums are A007716. Triangle of row sums is A320801. Triangle of column sums is A317533. Triangle of last columns (without its leading column 1,0,0,0,...) is A055884.

Cf. A000219, A008284, A316980, A316983, A318805, A319616, A320796, A321194.

A104601 Triangle T(r,n) read by rows: number of n X n (0,1)-matrices with exactly r entries equal to 1 and no zero row or columns.

Original entry on oeis.org

1, 0, 2, 0, 4, 6, 0, 1, 45, 24, 0, 0, 90, 432, 120, 0, 0, 78, 2248, 4200, 720, 0, 0, 36, 5776, 43000, 43200, 5040, 0, 0, 9, 9066, 222925, 755100, 476280, 40320, 0, 0, 1, 9696, 727375, 6700500, 13003620, 5644800, 362880, 0, 0, 0, 7480, 1674840

Offset: 1

Ralf Stephan, Mar 27 2005

			1
0,2
0,4,6
0,1,45,24
0,0,90,432,120
0,0,78,2248,4200,720
0,0,36,5776,43000,43200,5040
0,0,9,9066,222925,755100,476280,40320
0,0,1,9696,727375,6700500,13003620,5644800,362880
0,0,0,7480,1674840,37638036,179494350,226262400,71850240,3628800

M. Maia and M. Mendez, On the arithmetic product of combinatorial species, arXiv:math/0503436 [math.CO], 2005.

Right-edge diagonals include A000142, A055602, A055603. Row sums are in A104602.
Column sums are in A048291. The triangle read by columns = A055599.
Cf. A049311, A054976, A057150, A057151, A101370, A120732, A120733, A138178, A316983, A319616.

t[r_, n_] := Sum[ Sum[ (-1)^(2n - d - k/d)*Binomial[n, d]*Binomial[n, k/d]*Binomial[k, r], {d, Divisors[k]}], {k, r, n^2}]; Flatten[ Table[t[r, n], {r, 1, 10}, {n, 1, r}]] (* Jean-François Alcover, Jun 27 2012, from formula *)
Table[Length[Select[Subsets[Tuples[Range[n],2],{n}],Union[First/@#]==Union[Last/@#]==Range[k]&]],{n,6},{k,n}] (* Gus Wiseman, Nov 14 2018 *)

T(r, n) = Sum{l>=r, Sum{d|l, (-1)^(2n-d-l/d)*C(n, d)*C(n, l/d)*C(l, r) }}.

E.g.f.: Sum(((1+x)^n-1)^n*exp((1-(1+x)^n)*y)*y^n/n!,n=0..infinity). - Vladeta Jovovic, Feb 24 2008

A319639 Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

Original entry on oeis.org

1, 1, 1, 2, 20, 2043

Offset: 0

Gus Wiseman, Sep 25 2018

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.

			The a(1) = 1 through a(3) = 2 antichain covers:
1: {{1}}
2: {{1},{2}}
3: {{1},{2},{3}}
   {{1,2},{1,3},{2,3}}

Cf. A006126, A007716, A049311, A059201, A283877, A293606, A316980, A316983, A318099, A319558, A319616-A319646, A300913.

A321728 Number of integer partitions of n whose Young diagram cannot be partitioned into vertical sections of the same sizes as the parts of the original partition.

Original entry on oeis.org

0, 0, 1, 1, 2, 3, 5, 7, 10, 14, 20, 28, 37, 50

Offset: 0

Gus Wiseman, Nov 18 2018

First differs from A000701 at a(11) = 28, A000701(11) = 27
A vertical section is a partial Young diagram with at most one square in each row.
Conjecture: a(n) is the number of non-half-loop-graphical partitions of n. An integer partition is half-loop-graphical if it comprises the multiset of vertex-degrees of some graph with half-loops, where a half-loop is an edge with one vertex, to be distinguished from a full loop, which has two equal vertices.

			The a(2) = 1 through a(9) = 14 partitions whose Young diagram cannot be partitioned into vertical sections of the same sizes as the parts of the original partition are the same as the non-half-loop-graphical partitions up to n = 9:
  (2)  (3)  (4)   (5)   (6)    (7)    (8)     (9)
            (31)  (32)  (33)   (43)   (44)    (54)
                  (41)  (42)   (52)   (53)    (63)
                        (51)   (61)   (62)    (72)
                        (411)  (331)  (71)    (81)
                               (421)  (422)   (432)
                               (511)  (431)   (441)
                                      (521)   (522)
                                      (611)   (531)
                                      (5111)  (621)
                                              (711)
                                              (4311)
                                              (5211)
                                              (6111)
For example, a complete list of all half/full-loop-graphs with degrees y = (4,3,1) is the following:
  {{1,1},{1,2},{1,3},{2,2}}
  {{1},{2},{1,1},{1,2},{2,3}}
  {{1},{2},{1,1},{1,3},{2,2}}
  {{1},{3},{1,1},{1,2},{2,2}}
None of these is a half-loop-graph, as they have full loops (x,x), so y is counted under a(8).

Eric Weisstein's World of Mathematics, Degree Sequence.
Gus Wiseman, Counting and ranking factorizations, factorability, and vertex-degree partitions for groupings into pairs.

The complement is counted by A321729.
Cf. A000110, A000258, A000700, A000701, A008277, A046682, A319616, A321730, A321737, A321738.
The following pertain to the conjecture.
Half-loop-graphical partitions by length are A029889 or A339843 (covering).
The version for full loops is A339655.
A027187 counts partitions of even length, with Heinz numbers A028260.
A058696 counts partitions of even numbers, ranked by A300061.
A320663/A339888 count unlabeled multiset partitions into singletons/pairs.
A322661 counts labeled covering half-loop-graphs, ranked by A340018/A340019.
A339659 counts graphical partitions of 2n into k parts.
Cf. A006129, A025065, A062740, A095268, A096373, A167171, A320461, A338915, A339842, A339844, A339845.

spsu[,{}]:={{}};spsu[foo,set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,_}];
ptnpos[y_]:=Position[Table[1,{#}]&/@y,1];
ptnverts[y_]:=Select[Join@@Table[Subsets[ptnpos[y],{k}],{k,Reverse[Union[y]]}],UnsameQ@@First/@#&];
Table[Length[Select[IntegerPartitions[n],Select[spsu[ptnverts[#],ptnpos[#]],Function[p,Sort[Length/@p]==Sort[#]]]=={}&]],{n,8}]

a(n) is the number of integer partitions y of n such that the coefficient of m(y) in e(y) is zero, where m is monomial and e is elementary symmetric functions.

a(n) = A000041(n) - A321729(n).

A319748 Number of non-isomorphic set multipartitions (multisets of sets) of weight n with empty intersection.

Original entry on oeis.org

1, 0, 1, 3, 10, 25, 72, 182, 502, 1332, 3720, 10380, 30142, 88842, 270569, 842957, 2703060, 8885029, 29990388, 103743388, 367811233, 1334925589, 4957151327, 18817501736, 72972267232, 288863499000, 1166486601571, 4802115258807, 20141268290050, 86017885573548, 373852868791639

Offset: 0

Gus Wiseman, Sep 27 2018

nonn

The weight of a set multipartition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.

			Non-isomorphic representatives of the a(2) = 1 through a(4) = 10 set multipartitions:
  {{1},{2}}   {{1},{2,3}}     {{1},{2,3,4}}
             {{1},{2},{2}}    {{1,2},{3,4}}
             {{1},{2},{3}}   {{1},{1},{2,3}}
                             {{1},{2},{1,2}}
                             {{1},{2},{3,4}}
                             {{1},{3},{2,3}}
                            {{1},{1},{2},{2}}
                            {{1},{2},{2},{2}}
                            {{1},{2},{3},{3}}
                            {{1},{2},{3},{4}}

Andrew Howroyd, Table of n, a(n) for n = 0..50

Cf. A007716, A049311, A281116, A283877, A316980, A317752, A317755, A317757, A319616.

Cf. A319077, A319751, A319755, A319778, A319781, A319791.

WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
K(q, t, k)={WeighT(Vec(sum(j=1, #q, gcd(t, q[j])*x^lcm(t, q[j])) + O(x*x^k), -k))}
R(q, n)={vector(n, t, x*Ser(K(q, t, n)/t))}
a(n)={if(n==0, 1, my(s=0); forpart(q=n, my(u=R(q,n)); s+=permcount(q)*polcoef(exp(sum(t=1, n, u[t], O(x*x^n))) - exp(sum(t=1, n\2, x^t*u[t], O(x*x^n)))/(1-x), n)); s/n!)} \\ Andrew Howroyd, May 30 2023

Terms a(11) and beyond from Andrew Howroyd, May 30 2023

A319767 Number of non-isomorphic intersecting set systems spanning n vertices whose dual is also an intersecting set system.

Original entry on oeis.org

1, 1, 1, 5, 73

Offset: 0

Gus Wiseman, Sep 27 2018

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}}.
A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
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(1) = 1 through a(3) = 5 multiset partitions:
1: {{1}}
2: {{2},{1,2}}
3: {{3},{2,3},{1,2,3}}
   {{1,2},{1,3},{2,3}}
   {{1,3},{2,3},{1,2,3}}
   {{3},{1,3},{2,3},{1,2,3}}
   {{1,2},{1,3},{2,3},{1,2,3}}

Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.

Cf. A319752, A319765, A319766, A319768, A319769, A319773, A319774.

A321729 Number of integer partitions of n whose Young diagram can be partitioned into vertical sections of the same sizes as the parts of the original partition.

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 6, 8, 12, 16, 22, 28, 40, 51

Offset: 0

Gus Wiseman, Nov 18 2018

First differs from A046682 at a(11) = 28, A046682(11) = 29.
A vertical section is a partial Young diagram with at most one square in each row. For example, a suitable partition (shown as a coloring by positive integers) of the Young diagram of (322) is:
  1 2 3
  1 2
  2 3
Conjecture: a(n) is the number of half-loop-graphical partitions of n. An integer partition is half-loop-graphical if it comprises the multiset of vertex-degrees of some graph with half-loops, where a half-loop is an edge with one vertex, to be distinguished from a full loop, which has two equal vertices.

			The a(1) = 1 through a(8) = 12 partitions whose Young diagram cannot be partitioned into vertical sections of the same sizes as the parts of the original partition are the same as the half-loop-graphical partitions up to n = 8:
  (1)  (11)  (21)   (22)    (221)    (222)     (322)      (332)
             (111)  (211)   (311)    (321)     (2221)     (2222)
                    (1111)  (2111)   (2211)    (3211)     (3221)
                            (11111)  (3111)    (4111)     (3311)
                                     (21111)   (22111)    (4211)
                                     (111111)  (31111)    (22211)
                                               (211111)   (32111)
                                               (1111111)  (41111)
                                                          (221111)
                                                          (311111)
                                                          (2111111)
                                                          (11111111)
For example, the half-loop-graphs
  {{1},{1,2},{1,3},{2,3}}
  {{1},{2},{3},{1,2},{1,3}}
both have degrees y = (3,2,2), so y is counted under a(7).

The complement is counted by A321728.
Cf. A000110, A000258, A000700, A000701, A006052, A007016, A008277, A046682, A319056, A319616, A321730, A321737, A321738.
The following pertain to the conjecture.
Half-loop-graphical partitions by length are A029889 or A339843 (covering).
The version for full loops is A339656.
A027187 counts partitions of even length, ranked by A028260.
A058696 counts partitions of even numbers, ranked by A300061.
A320663/A339888 count unlabeled multiset partitions into singletons/pairs.
A322661 counts labeled covering half-loop-graphs, ranked by A340018/A340019.
A339659 is a triangle counting graphical partitions by length.
Cf. A006129, A025065, A062740, A095268, A096373, A167171, A320461, A338915, A339842, A339844, A339845.

spsu[,{}]:={{}};spsu[foo,set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,_}];
ptnpos[y_]:=Position[Table[1,{#}]&/@y,1];
ptnverts[y_]:=Select[Join@@Table[Subsets[ptnpos[y],{k}],{k,Reverse[Union[y]]}],UnsameQ@@First/@#&];
Table[Length[Select[IntegerPartitions[n],Length[Select[spsu[ptnverts[#],ptnpos[#]],Function[p,Sort[Length/@p]==Sort[#]]]]>0&]],{n,8}]

a(n) is the number of integer partitions y of n such that the coefficient of m(y) in e(y) is nonzero, where m is monomial symmetric functions and e is elementary symmetric functions.

a(n) = A000041(n) - A321728(n).

cp's OEIS Frontend

A340600 Number of non-isomorphic balanced multiset partitions of weight n.

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A057150 Triangle read by rows: T(n,k) = number of k X k binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

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A320328 Number of square multiset partitions of integer partitions of n.

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A320808 Regular tetrangle where T(n,k,i) is the number of nonnegative integer matrices up to row and column permutations with no zero rows or columns and k nonzero entries summing to n, with i columns.

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A104601 Triangle T(r,n) read by rows: number of n X n (0,1)-matrices with exactly r entries equal to 1 and no zero row or columns.

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A319639 Number of antichain covers of n vertices by distinct sets whose dual is also an antichain of distinct sets.

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A321728 Number of integer partitions of n whose Young diagram cannot be partitioned into vertical sections of the same sizes as the parts of the original partition.

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A319748 Number of non-isomorphic set multipartitions (multisets of sets) of weight n with empty intersection.

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A319767 Number of non-isomorphic intersecting set systems spanning n vertices whose dual is also an intersecting set system.

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