A306018 -id:A306018 - cp's OEIS frontend

A306017 Number of non-isomorphic multiset partitions of weight n in which all parts have the same size.

1, 1, 4, 6, 17, 14, 66, 30, 189, 222, 550, 112, 4696, 202, 5612, 30914, 63219, 594, 453125, 980, 3602695, 5914580, 1169348, 2510, 299083307, 232988061, 23248212, 2669116433, 14829762423, 9130, 170677509317, 13684, 1724710753084, 2199418340875, 14184712185, 38316098104262

Offset: 0

Gus Wiseman, Jun 17 2018

nonn

A multiset partition of weight n is a finite multiset of finite nonempty multisets whose sizes sum to n.
Number of distinct nonnegative integer matrices with all row sums equal and total sum n up to row and column permutations. - Andrew Howroyd, Sep 05 2018
From Gus Wiseman, Oct 11 2018: (Start)
Also the number of non-isomorphic multiset partitions of weight n in which each vertex appears the same number of times. For n = 4, non-isomorphic representatives of these 17 multiset partitions are:
  {{1,1,1,1}}
  {{1,1,2,2}}
  {{1,2,3,4}}
  {{1},{1,1,1}}
  {{1},{1,2,2}}
  {{1},{2,3,4}}
  {{1,1},{1,1}}
  {{1,1},{2,2}}
  {{1,2},{1,2}}
  {{1,2},{3,4}}
  {{1},{1},{1,1}}
  {{1},{1},{2,2}}
  {{1},{2},{1,2}}
  {{1},{2},{3,4}}
  {{1},{1},{1},{1}}
  {{1},{1},{2},{2}}
  {{1},{2},{3},{4}}
(End)

			Non-isomorphic representatives of the a(4) = 17 multiset partitions:
  {{1,1,1,1}}
  {{1,1,2,2}}
  {{1,2,2,2}}
  {{1,2,3,3}}
  {{1,2,3,4}}
  {{1,1},{1,1}}
  {{1,1},{2,2}}
  {{1,2},{1,2}}
  {{1,2},{2,2}}
  {{1,2},{3,3}}
  {{1,2},{3,4}}
  {{1,3},{2,3}}
  {{1},{1},{1},{1}}
  {{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. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306018, A306019, A306020, A306021, A318951.

Cf. A064573, A279787, A305551, A319616, A319056, A331485.

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];
K[q_List, t_, k_] := SeriesCoefficient[1/Product[g = GCD[t, q[[j]]]; (1 - x^(q[[j]]/g))^g, {j, 1, Length[q]}], {x, 0, k}];
RowSumMats[n_, m_, k_] := Module[{s = 0}, Do[s += permcount[q]* SeriesCoefficient[Exp[Sum[K[q, t, k]/t*x^t, {t, 1, n}]], {x, 0, n}], {q, IntegerPartitions[m]}]; s/m!];
a[n_] := a[n] = If[n==0, 1, If[PrimeQ[n], 2 PartitionsP[n], Sum[ RowSumMats[ n/d, n, d], {d, Divisors[n]}]]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 07 2019, after Andrew Howroyd *)

\\ See A318951 for RowSumMats.
a(n)={sumdiv(n,d,RowSumMats(n/d,n,d))} \\ Andrew Howroyd, Sep 05 2018

For p prime, a(p) = 2*A000041(p).

a(n) = Sum_{d|n} A331485(n/d, d). - Andrew Howroyd, Feb 09 2020

Terms a(11) and beyond from Andrew Howroyd, Sep 05 2018

A306021 Number of set-systems spanning {1,...,n} in which all sets have the same size.

Original entry on oeis.org

1, 1, 2, 6, 54, 1754, 1102746, 68715913086, 1180735735356265746734, 170141183460507906731293351306656207090, 7237005577335553223087828975127304177495735363998991435497132232365910414322

Offset: 0

Gus Wiseman, Jun 17 2018

nonn

a(n) is the number of labeled uniform hypergraphs spanning n vertices. - Andrew Howroyd, Jan 16 2024

			The a(3) = 6 set-systems in which all sets have the same size:
  {{1,2,3}}
  {{1}, {2}, {3}}
  {{1,2}, {1,3}}
  {{1,2}, {2,3}}
  {{1,3}, {2,3}}
  {{1,2}, {1,3}, {2,3}}

Andrew Howroyd, Table of n, a(n) for n = 0..14

Row sums of A299471.
The unlabeled version is A301481.
The connected version is A299353.
Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306019, A306020.

Table[Sum[(-1)^(n-k)*Binomial[n,k]*(1+Sum[2^Binomial[k,d]-1,{d,k}]),{k,0,n}],{n,12}]

a(n) = if(n==0, 1, sum(k=0, n, sum(d=0, n, (-1)^(n-d)*binomial(n,d)*2^binomial(d,k)))) \\ Andrew Howroyd, Jan 16 2024

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

Inverse binomial transform of A306020. - Andrew Howroyd, Jan 16 2024

A299471 Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 41, 11, 1, 1, 768, 958, 26, 1, 1, 27449, 1042642, 32596, 57, 1, 1, 1887284, 34352419335, 34359509614, 2096731, 120, 1, 1, 252522481, 72057319189324805, 1180591620442534312297, 72057594021152435, 268434467, 247, 1, 1, 66376424160

Offset: 1

Gus Wiseman, Jun 18 2018

			Triangle begins:
  1;
  1,     1;
  1,     4,       1;
  1,    41,      11,     1;
  1,   768,     958,    26,  1;
  1, 27449, 1042642, 32596, 57, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..91 (rows 1..13)
Wikipedia, Hypergraph

Columns 1..4 are A000012, A006129, A302374, A302396.
Row sums are A306021.
The unlabeled version is A301922.
The connected version is A299354.
Cf. A000005, A001315, A006126, A038041, A298422, A298426, A306017, A306018, A306019, A306020.

Table[Sum[(-1)^(n-d)*Binomial[n,d]*2^Binomial[d,k],{d,0,n}],{n,10},{k,n}]

T(n, k) = sum(d = 0, n, (-1)^(n-d)*binomial(n,d)*2^binomial(d,k)) \\ Andrew Howroyd, Jan 16 2024

T(n, k) = Sum_{d = 0..n} (-1)^(n-d)*binomial(n,d)*2^binomial(d,k).

A331461 Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 5, 8, 4, 1, 1, 1, 7, 23, 16, 5, 1, 1, 1, 11, 66, 93, 30, 6, 1, 1, 1, 15, 212, 652, 332, 50, 7, 1, 1, 1, 22, 686, 6369, 6414, 1062, 80, 8, 1, 1, 1, 30, 2389, 79568, 226041, 56712, 3117, 120, 9, 1, 1, 1, 42, 8682, 1256425, 12848128, 7295812, 441881, 8399, 175, 10, 1, 1

Offset: 0

Andrew Howroyd, Jan 18 2020

A(n,k) is the number of non-isomorphic set multipartitions (multiset of sets) with k parts each part has size n.

			Array begins:
===========================================================
n\k | 0 1 2   3    4       5          6              7
----+-----------------------------------------------------
  0 | 1 1 1   1    1       1          1              1 ...
  1 | 1 1 2   3    5       7         11             15 ...
  2 | 1 1 3   8   23      66        212            686 ...
  3 | 1 1 4  16   93     652       6369          79568 ...
  4 | 1 1 5  30  332    6414     226041       12848128 ...
  5 | 1 1 6  50 1062   56712    7295812     1817321457 ...
  6 | 1 1 7  80 3117  441881  195486906   200065951078 ...
  7 | 1 1 8 120 8399 3006771 4298181107 17131523059493 ...
  ...
The A(2,3) = 8 matrices are:
  [1 0 0]  [1 1 0]  [1 1 1]  [1 1 0]  [1 1 0]  [1 1 1]  [1 1 0]  [1 1 1]
  [1 0 0]  [1 0 0]  [1 0 0]  [1 1 0]  [1 0 1]  [1 1 0]  [1 0 1]  [1 1 1]
  [0 1 0]  [0 1 0]  [0 1 0]  [0 0 1]  [0 1 0]  [0 0 1]  [0 1 1]
  [0 1 0]  [0 0 1]  [0 0 1]  [0 0 1]  [0 0 1]
  [0 0 1]  [0 0 1]
  [0 0 1]

Andrew Howroyd, Table of n, a(n) for n = 0..152

Rows n=0..6 are A000012, A000041, A050535, A050913, A058783, A058784, A058785.
Columns k=0..4 are A000012, A000012, A000027(n+1), A002624, A331720.
Cf. A188392, A262809, A304942, A306018, A330942, A331485, A331508, A331509, A331510.

\\ See A304942 for Blocks
T(n,k)={Blocks(k, n*k, n)}
{ for(n=0, 7, for(k=0, 6, print1(T(n,k), ", ")); print) }

A306018(n) = Sum_{d|n} A(n/d, d).

A306019 Number of non-isomorphic set-systems of weight n in which all parts have the same size.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 10, 2, 17, 14, 33, 2, 167, 2, 186, 491, 785, 2, 5839, 2, 11123, 53454, 15229, 2, 1102924, 53537, 193382, 16334183, 12411062, 2, 382413555, 2, 993814248, 9763321547, 53394774, 1778595972, 402119882757, 2, 1111261718, 9674133468473, 16955983996383

Offset: 0

Gus Wiseman, Jun 17 2018

nonn

A set-system of weight n is a finite set of finite nonempty sets whose sizes sum to n.

			Non-isomorphic representatives of the a(6) = 10 set-systems:
{{1,2,3,4,5,6}}
{{1,2,3},{4,5,6}}
{{1,2,5},{3,4,5}}
{{1,3,4},{2,3,4}}
{{1,2},{1,3},{2,3}}
{{1,2},{3,4},{5,6}}
{{1,2},{3,5},{4,5}}
{{1,3},{2,4},{3,4}}
{{1,4},{2,4},{3,4}}
{{1},{2},{3},{4},{5},{6}}

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

Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306020, A306021.

\\ See A331508 for T(n,k).
a(n) = {if(n==0, 1, sumdiv(n, d, if(d==1 || d==n, 1, T(n/d, d))))} \\ Andrew Howroyd, Jan 16 2024

a(p) = 2 for prime p. - Andrew Howroyd, Aug 29 2019

a(n) = Sum_{d|n} A331508(n/d, d) for n > 0. - Andrew Howroyd, Jan 16 2024

Terms a(12) and beyond from Andrew Howroyd, Sep 01 2019

A306020 a(n) is the number of set-systems using nonempty subsets of {1,...,n} in which all sets have the same size.

Original entry on oeis.org

1, 2, 5, 16, 95, 2110, 1114237, 68723671292, 1180735735906024030715, 170141183460507917357914971986913657850, 7237005577335553223087828975127304179197147198604070555943173844710572689401

Offset: 0

Gus Wiseman, Jun 17 2018

nonn

A058673(n) <= a(n). - Lorenzo Sauras Altuzarra, Aug 10 2023

			a(3) = 16 set-systems in which all sets have the same size:
  {}
  {{1}}
  {{2}}
  {{3}}
  {{1,2}}
  {{1,3}}
  {{2,3}}
  {{1,2,3}}
  {{1},{2}}
  {{1},{3}}
  {{2},{3}}
  {{1,2},{1,3}}
  {{1,2},{2,3}}
  {{1,3},{2,3}}
  {{1},{2},{3}}
  {{1,2},{1,3},{2,3}}

Index entries for sequences related to matroids

Cf. A000005, A001315, A007716, A038041, A049311, A058673 (labeled matroids), A283877, A298422, A306017, A306018, A306019, A306021.

Row sums of A059328.

a := n -> 1-n+add(2^binomial(n, d), d = 1 .. n):
seq(a(n), n = 0 .. 10); # Lorenzo Sauras Altuzarra, Aug 11 2023

Table[1+Sum[2^Binomial[n,d]-1,{d,n}],{n,10}]

a(n) = 1 - n + sum(d = 1, n, 2^binomial(n, d)); \\ Michel Marcus, Aug 10 2023

a(n) = 1 - n + Sum_{d = 1..n} 2^binomial(n, d).

A322785 Number of uniform multiset partitions of uniform multisets of size n whose union is an initial interval of positive integers.

Original entry on oeis.org

1, 1, 4, 4, 12, 4, 48, 4, 183, 297, 1186, 4, 33950, 4, 139527, 1529608, 4726356, 4, 229255536, 4, 3705777010, 36279746314, 13764663019, 4, 14096735197959, 5194673049514, 7907992957755, 2977586461058927, 13426396910491001, 4, 1350012288268171854, 4, 59487352224070807287

Offset: 0

Gus Wiseman, Dec 26 2018

nonn

A multiset is uniform if all multiplicities are equal. A multiset partition is uniform if all parts have the same size.

			The a(1) = 1 though a(6) = 48 multiset partitions:
  {1}  {11}    {111}      {1111}        {11111}          {111111}
       {12}    {123}      {1122}        {12345}          {111222}
       {1}{1}  {1}{1}{1}  {1234}        {1}{1}{1}{1}{1}  {112233}
       {1}{2}  {1}{2}{3}  {11}{11}      {1}{2}{3}{4}{5}  {123456}
                          {11}{22}                       {111}{111}
                          {12}{12}                       {111}{222}
                          {12}{34}                       {112}{122}
                          {13}{24}                       {112}{233}
                          {14}{23}                       {113}{223}
                          {1}{1}{1}{1}                   {122}{133}
                          {1}{1}{2}{2}                   {123}{123}
                          {1}{2}{3}{4}                   {123}{456}
                                                         {124}{356}
                                                         {125}{346}
                                                         {126}{345}
                                                         {134}{256}
                                                         {135}{246}
                                                         {136}{245}
                                                         {145}{236}
                                                         {146}{235}
                                                         {156}{234}
                                                         {11}{11}{11}
                                                         {11}{12}{22}
                                                         {11}{22}{33}
                                                         {11}{23}{23}
                                                         {12}{12}{12}
                                                         {12}{12}{33}
                                                         {12}{13}{23}
                                                         {12}{34}{56}
                                                         {12}{35}{46}
                                                         {12}{36}{45}
                                                         {13}{13}{22}
                                                         {13}{24}{56}
                                                         {13}{25}{46}
                                                         {13}{26}{45}
                                                         {14}{23}{56}
                                                         {14}{25}{36}
                                                         {14}{26}{35}
                                                         {15}{23}{46}
                                                         {15}{24}{36}
                                                         {15}{26}{34}
                                                         {16}{23}{45}
                                                         {16}{24}{35}
                                                         {16}{25}{34}
                                                         {1}{1}{1}{1}{1}{1}
                                                         {1}{1}{1}{2}{2}{2}
                                                         {1}{1}{2}{2}{3}{3}
                                                         {1}{2}{3}{4}{5}{6}

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

Row sums of A322788.

Cf. A000040, A038041, A072774, A100778, A299353, A306017, A306018, A306021, A317583, A317584, A319056, A319189, A321721, A322705, A322784, A322788.

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[Sum[Length[Select[mps[m],SameQ@@Length/@#&]],{m,Table[Join@@Table[Range[n/d],{d}],{d,Divisors[n]}]}],{n,8}]

a(n) = 4 <=> n in { A000040 }. - Alois P. Heinz, Feb 03 2022

More terms from Alois P. Heinz, Jan 30 2019

Terms a(14) and beyond from Andrew Howroyd, Feb 03 2022

A317584 Number of multiset partitions of strongly normal multisets of size n such that all blocks have the same size.

Original entry on oeis.org

1, 4, 6, 19, 14, 113, 30, 584, 1150, 4023, 112, 119866, 202, 432061, 5442765, 16646712, 594, 738090160, 980, 13160013662, 113864783987, 39049423043, 2510, 44452496723053, 19373518220009, 21970704599961, 8858890258339122, 43233899006497146, 9130, 4019875470540832643

Offset: 1

Gus Wiseman, Aug 01 2018

nonn

A multiset is strongly normal if it spans an initial interval of positive integers with weakly decreasing multiplicities.

			The a(4) = 19 multiset partitions:
  {{1,1,1,1}}, {{1,1},{1,1}}, {{1},{1},{1},{1}},
  {{1,1,1,2}}, {{1,1},{1,2}}, {{1},{1},{1},{2}},
  {{1,1,2,2}}, {{1,1},{2,2}}, {{1,2},{1,2}}, {{1},{1},{2},{2}},
  {{1,1,2,3}}, {{1,1},{2,3}}, {{1,2},{1,3}}, {{1},{1},{2},{3}},
  {{1,2,3,4}}, {{1,2},{3,4}}, {{1,3},{2,4}}, {{1,4},{2,3}}, {{1},{2},{3},{4}}.

Cf. A000005, A000041, A007716, A038041, A255906, A298422, A306017, A306018, A306019, A306020, A306021, A317583.

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]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2,{#1}]&,#]]&/@IntegerPartitions[n];
Table[Length[Select[Join@@mps/@strnorm[n],SameQ@@Length/@#&]],{n,6}]

\\ See links in A339645 for combinatorial species functions.
cycleIndex(n)={sum(n=1, n, x^n*sumdiv(n, d, sApplyCI(symGroupCycleIndex(d), d, symGroupCycleIndex(n/d), n/d))) + O(x*x^n)}
StronglyNormalLabelingsSeq(cycleIndex(15)) \\ Andrew Howroyd, Jan 01 2021

a(p) = 2*A000041(p) for prime p. - Andrew Howroyd, Jan 01 2021

Terms a(9) and beyond from Andrew Howroyd, Jan 01 2021

A322787 Irregular triangle read by rows where T(n,k) is the number of non-isomorphic multiset partitions of a multiset with d = A027750(n, k) copies of each integer from 1 to n/d.

Original entry on oeis.org

1, 2, 2, 3, 3, 5, 7, 5, 7, 7, 11, 23, 21, 11, 15, 15, 22, 79, 66, 22, 30, 162, 30, 42, 274, 192, 42, 56, 56, 77, 1003, 1636, 1338, 565, 77, 101, 101, 135, 3763, 1579, 135, 176, 19977, 10585, 176, 231, 14723, 43686, 4348, 231, 297, 297, 385, 59663, 298416, 82694, 11582, 385

Offset: 1

Gus Wiseman, Dec 26 2018

			Triangle begins:
   1
   2   2
   3   3
   5   7   5
   7   7
  11  23  21  11
  15  15
  22  79  66  22
  30 162  30
  42 274 192  42
Non-isomorphic representatives of the multiset partitions counted under row 6:
{123456}           {112233}           {111222}           {111111}
{1}{23456}         {1}{12233}         {1}{11222}         {1}{11111}
{12}{3456}         {11}{2233}         {11}{1222}         {11}{1111}
{123}{456}         {112}{233}         {111}{222}         {111}{111}
{1}{2}{3456}       {12}{1233}         {112}{122}         {1}{1}{1111}
{1}{23}{456}       {123}{123}         {12}{1122}         {1}{11}{111}
{12}{34}{56}       {1}{1}{2233}       {1}{1}{1222}       {11}{11}{11}
{1}{2}{3}{456}     {1}{12}{233}       {1}{11}{222}       {1}{1}{1}{111}
{1}{2}{34}{56}     {11}{22}{33}       {11}{12}{22}       {1}{1}{11}{11}
{1}{2}{3}{4}{56}   {11}{23}{23}       {1}{12}{122}       {1}{1}{1}{1}{11}
{1}{2}{3}{4}{5}{6} {1}{2}{1233}       {1}{2}{1122}       {1}{1}{1}{1}{1}{1}
                   {12}{13}{23}       {12}{12}{12}
                   {1}{23}{123}       {2}{11}{122}
                   {2}{11}{233}       {1}{1}{1}{222}
                   {1}{1}{2}{233}     {1}{1}{12}{22}
                   {1}{1}{22}{33}     {1}{1}{2}{122}
                   {1}{1}{23}{23}     {1}{2}{11}{22}
                   {1}{2}{12}{33}     {1}{2}{12}{12}
                   {1}{2}{13}{23}     {1}{1}{1}{2}{22}
                   {1}{2}{3}{123}     {1}{1}{2}{2}{12}
                   {1}{1}{2}{2}{33}   {1}{1}{1}{2}{2}{2}
                   {1}{1}{2}{3}{23}
                   {1}{1}{2}{2}{3}{3}

Andrew Howroyd, Table of n, a(n) for n = 1..207 (rows 1..50)

Row sums are A306017. First column is A000041.

Cf. A001055, A005176, A027750, A056239, A072774, A100778, A295193, A306018, A318951, A319190, A319612, A322784, A322785, A322788, A322792.

\\ See A318951 for RowSumMats
row(n)={my(d=divisors(n)); vector(#d, i, RowSumMats(n/d[i], n, d[i]))}
{ for(n=1, 15, print(row(n))) } \\ Andrew Howroyd, Feb 02 2022

Terms a(28) and beyond from Andrew Howroyd, Feb 02 2022

Name edited by Peter Munn, Mar 05 2025

A322789 Irregular triangle read by rows where T(n,k) is the number of non-isomorphic uniform multiset partitions of a multiset with d = A027750(n,k) copies of each integer from 1 to n/d.

Original entry on oeis.org

1, 2, 2, 2, 2, 3, 4, 3, 2, 2, 4, 7, 6, 4, 2, 2, 4, 10, 8, 4, 3, 7, 3, 4, 12, 8, 4, 2, 2, 6, 32, 35, 31, 18, 6, 2, 2, 4, 21, 10, 4, 4, 47, 29, 4, 5, 49, 72, 19, 5, 2, 2, 6, 81, 170, 71, 24, 6, 2, 2, 6, 138, 478, 296, 32, 6, 4, 429, 76, 4, 4, 64, 14, 4

Offset: 1

Gus Wiseman, Dec 26 2018

A multiset partition is uniform if all parts have the same size.

			Triangle begins:
  1
  2  2
  2  2
  3  4  3
  2  2
  4  7  6  4
  2  2
  4 10  8  4
  3  7  3
  4 12  8  4
Non-isomorphic representatives of the multiset partitions counted under row 6:
{123456}           {112233}           {111222}           {111111}
{123}{456}         {112}{233}         {111}{222}         {111}{111}
{12}{34}{56}       {123}{123}         {112}{122}         {11}{11}{11}
{1}{2}{3}{4}{5}{6} {11}{22}{33}       {11}{12}{22}       {1}{1}{1}{1}{1}{1}
                   {11}{23}{23}       {12}{12}{12}
                   {12}{13}{23}       {1}{1}{1}{2}{2}{2}
                   {1}{1}{2}{2}{3}{3}

Andrew Howroyd, Table of n, a(n) for n = 1..338 (rows 1..75)

Row sums are A319056. First column is A000005.

Cf. A001055, A005176, A027750, A056239, A072774, A100778, A295193, A306017, A306018, A319190, A319612, A322784, A322785, A322787, A322792.

Terms a(28) and beyond from Andrew Howroyd, Feb 03 2022

Name edited by Peter Munn, Mar 05 2025

cp's OEIS Frontend

A306017 Number of non-isomorphic multiset partitions of weight n in which all parts have the same size.

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A306021 Number of set-systems spanning {1,...,n} in which all sets have the same size.

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A299471 Regular triangle where T(n,k) is the number of labeled k-uniform hypergraphs spanning n vertices.

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A331461 Array read by antidiagonals: A(n,k) is the number of nonequivalent binary matrices with k columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.

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A306019 Number of non-isomorphic set-systems of weight n in which all parts have the same size.

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A306020 a(n) is the number of set-systems using nonempty subsets of {1,...,n} in which all sets have the same size.

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A322785 Number of uniform multiset partitions of uniform multisets of size n whose union is an initial interval of positive integers.

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