A306017 -id:A306017 - cp's OEIS frontend

A301924 Regular triangle where T(n,k) is the number of unlabeled k-uniform connected hypergraphs spanning n vertices.

1, 0, 1, 0, 2, 1, 0, 6, 3, 1, 0, 21, 29, 4, 1, 0, 112, 2101, 150, 5, 1, 0, 853, 7011181, 7013164, 1037, 6, 1, 0, 11117, 1788775603301, 29281354507753847, 1788782615612, 12338, 7, 1, 0, 261080, 53304526022885278403, 234431745534048893449761040648508, 234431745534048922729326772799024, 53304527811667884902, 274659, 8, 1

Offset: 1

Gus Wiseman, Jun 19 2018

			Triangle begins:
   1
   0    1
   0    2       1
   0    6       3       1
   0   21      29       4    1
   0  112    2101     150    5 1
   0  853 7011181 7013164 1037 6 1
   ...
The T(4,2) = 6 hypergraphs:
  {{1,3},{2,4},{3,4}}
  {{1,4},{2,4},{3,4}}
  {{1,2},{1,3},{2,4},{3,4}}
  {{1,4},{2,3},{2,4},{3,4}}
  {{1,3},{1,4},{2,3},{2,4},{3,4}}
  {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}

Row sums are A301920.
Columns k=2..3 are A001349(n > 1), A003190(n > 1).
Cf. A003465, A006129, A038041, A055621, A298422, A299353, A299354, A299471, A301481, A301922, A306017-A306021, A309858.

InvEulerT(v)={my(p=log(1+x*Ser(v))); dirdiv(vector(#v,n,polcoeff(p,n)), vector(#v,n,1/n))}
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}
rep(typ)={my(L=List(), k=0); for(i=1, #typ, k+=typ[i]; listput(L, k); while(#L0, u=vecsort(apply(f, u)); d=lex(u, v)); !d}
Q(n, k, perm)={my(t=0); forsubset([n, k], v, t += can(Vec(v), t->perm[t])); t}
U(n, k)={my(s=0); forpart(p=n, s += permcount(p)*2^Q(n, k, rep(p))); s/n!}
A(n)={Mat(vector(n, k, InvEulerT(vector(n,i,U(i,k)-U(i-1,k)))~))}
{ my(T=A(8)); for(n=1, #T, print(T[n,1..n])) } \\ Andrew Howroyd, Aug 26 2019

Column k is the inverse Euler transform of column k of A301922. - Andrew Howroyd, Aug 26 2019

Terms a(16) and beyond from Andrew Howroyd, Aug 26 2019

A305552 Number of uniform normal multiset partitions of weight n.

Original entry on oeis.org

1, 1, 3, 5, 12, 17, 47, 65, 170, 277, 655, 1025, 2739, 4097, 10281, 17257, 41364, 65537, 170047, 262145, 660296, 1094457, 2621965, 4194305, 10898799, 16792721, 41945103, 69938141, 168546184, 268435457, 694029255, 1073741825, 2696094037, 4474449261, 10737451027

Offset: 0

Gus Wiseman, Jun 20 2018

nonn

A multiset is normal if it spans an initial interval of positive integers. A multiset partition m is uniform if all parts have the same size, and normal if all parts are normal. The weight of m is the sum of sizes of its parts.

			The a(4) = 12 uniform normal multiset partitions:
{1111}, {1222}, {1122}, {1112}, {1233}, {1223}, {1123}, {1234},
{11,11}, {11,12}, {12,12},
{1,1,1,1}.

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

Cf. A000005, A001315, A007716, A034691, A038041, A074854, A289078, A305552, A306017.

Table[Sum[Binomial[2^(n/k-1)+k-1,k],{k,Divisors[n]}],{n,35}]

a(n)={if(n<1, n==0, sumdiv(n, d, binomial(2^(n/d - 1) + d - 1, d)))} \\ Andrew Howroyd, Jun 22 2018

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

A306318 Number of square twice-partitions of n.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 4, 5, 10, 12, 19, 24, 39, 49, 73, 104, 151, 212, 317, 443, 638, 936, 1296, 1841, 2635, 3641, 5069, 7176, 9884, 13614, 19113, 26162, 36603, 50405, 70153, 96176, 135388, 184753, 257882, 353587, 494653, 671992, 934905, 1272195, 1762979, 2389255

Offset: 0

Gus Wiseman, Feb 07 2019

nonn

A twice partition of n is a sequence of integer partitions, one of each part in an integer partition of n. It is square if the number of parts is equal to the number of parts in each part.

			The a(10) = 19 square twice-partitions:
  ((ten))  ((32)(32))  ((211)(111)(111))
           ((32)(41))
           ((33)(22))
           ((33)(31))
           ((41)(32))
           ((41)(41))
           ((42)(22))
           ((42)(31))
           ((43)(21))
           ((44)(11))
           ((51)(22))
           ((51)(31))
           ((52)(21))
           ((53)(11))
           ((61)(21))
           ((62)(11))
           ((71)(11))

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Cf. A000219, A001970, A063834 (twice-partitions), A089299 (square plane partitions), A279787, A305551, A306017, A306319 (rectangular twice-partitions), A319066, A323429, A323531 (square partitions of partitions).

Table[Sum[Length[Union@@(Tuples[IntegerPartitions[#,{k}]&/@#]&/@IntegerPartitions[n,{k}])],{k,0,Sqrt[n]}],{n,0,20}]

A322531 Heinz numbers of integer partitions whose parts all have the same number of prime factors (counted with or without multiplicity) and whose product of parts is a squarefree number.

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 11, 13, 15, 16, 17, 29, 31, 32, 33, 41, 43, 47, 51, 55, 59, 64, 67, 73, 79, 83, 85, 93, 101, 109, 113, 123, 127, 128, 137, 139, 149, 155, 157, 163, 165, 167, 177, 179, 181, 187, 191, 199, 201, 205, 211, 233, 241, 249, 255, 256, 257, 269, 271

Offset: 1

Gus Wiseman, Dec 14 2018

nonn

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
All entries are themselves squarefree numbers (except the powers of 2).
The first odd term not in this sequence but in A302521 is 141, which is the MM-number (see A302242) of {{1},{2,3}}.

			The sequence of all integer partitions whose parts all have the same number of prime factors and whose product of parts is a squarefree number begins: (), (1), (2), (1,1), (3), (1,1,1), (5), (6), (3,2), (1,1,1,1), (7), (10), (11), (1,1,1,1,1), (5,2), (13), (14), (15), (7,2), (5,3), (17), (1,1,1,1,1,1).

Cf. A003963, A005117, A038041, A056239, A073576, A112798, A302242, A302505, A306017, A319056, A319169, A320324, A321717, A321718, A322526, A322528.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],And[SameQ@@PrimeOmega/@primeMS[#],SquareFreeQ[Times@@primeMS[#]]]&]

A322703 Squarefree MM-numbers of strict uniform regular multiset systems spanning an initial interval of positive integers.

Original entry on oeis.org

1, 2, 3, 7, 13, 15, 19, 53, 113, 131, 151, 161, 165, 311, 719, 1291, 1321, 1619, 1937, 1957, 2021, 2093, 2117, 2257, 2805, 3671, 6997, 8161, 10627, 13969, 13987, 14023, 15617, 17719, 17863, 20443, 22207, 22339, 38873, 79349, 84017, 86955, 180503, 202133

Offset: 1

Gus Wiseman, Dec 27 2018

nonn

A multiset multisystem is a finite multiset of finite multisets. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.

A multiset multisystem is uniform if all parts have the same size, regular if all vertices appear the same number of times, and strict if there are no repeated parts. For example, {{1,1},{2,3},{2,3}} is uniform and regular but not strict, so its MM-number 15463 does not belong to the sequence. Note that the parts of parts such as {1,1} do not have to be distinct, only the multiset of parts.

			The sequence of all strict uniform regular multiset multisystems spanning an initial interval of positive integers, together with their MM-numbers, begins:
      1: {}
      2: {{}}
      3: {{1}}
      7: {{1,1}}
     13: {{1,2}}
     15: {{1},{2}}
     19: {{1,1,1}}
     53: {{1,1,1,1}}
    113: {{1,2,3}}
    131: {{1,1,1,1,1}}
    151: {{1,1,2,2}}
    161: {{1,1},{2,2}}
    165: {{1},{2},{3}}
    311: {{1,1,1,1,1,1}}
    719: {{1,1,1,1,1,1,1}}
   1291: {{1,2,3,4}}
   1321: {{1,1,1,2,2,2}}
   1619: {{1,1,1,1,1,1,1,1}}
   1937: {{1,2},{3,4}}
   1957: {{1,1,1},{2,2,2}}
   2021: {{1,4},{2,3}}
   2093: {{1,1},{1,2},{2,2}}
   2117: {{1,3},{2,4}}
   2257: {{1,1,2},{1,2,2}}
   2805: {{1},{2},{3},{4}}
   3671: {{1,1,1,1,1,1,1,1,1}}
   6997: {{1,1,2,2,3,3}}
   8161: {{1,1,1,1,1,1,1,1,1,1}}
  10627: {{1,1,1,1,2,2,2,2}}
  13969: {{1,2,2},{1,3,3}}
  13987: {{1,1,3},{2,2,3}}
  14023: {{1,1,2},{2,3,3}}
  15617: {{1,1},{2,2},{3,3}}
  17719: {{1,2},{1,3},{2,3}}
  17863: {{1,1,1,1,1,1,1,1,1,1,1}}

Cf. A005117, A007016, A112798, A302242, A306017, A306021, A319056, A319189, A319190, A320324, A321698, A321699, A322554, A322833.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
normQ[sys_]:=Or[Length[sys]==0,Union@@sys==Range[Max@@Max@@sys]];
Select[Range[1000],And[SquareFreeQ[#],normQ[primeMS/@primeMS[#]],SameQ@@PrimeOmega/@primeMS[#],SameQ@@Last/@FactorInteger[Times@@primeMS[#]]]&]

A322786 Irregular triangle read by rows where T(n,k) is the number of 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, 5, 3, 15, 9, 5, 52, 7, 203, 66, 31, 11, 877, 15, 4140, 712, 109, 22, 21147, 686, 30, 115975, 10457, 339, 42, 678570, 56, 4213597, 198091, 27036, 6721, 1043, 77, 27644437, 101, 190899322, 4659138, 2998, 135, 1382958545, 1688360, 58616, 176

Offset: 1

Gus Wiseman, Dec 26 2018

			Triangle begins:
        1
        2       2
        5       3
       15       9       5
       52       7
      203      66      31      11
      877      15
     4140     712     109      22
    21147     686      30
   115975   10457     339      42
   678570      56
  4213597  198091   27036    6721    1043      77
For example, row 4 counts the following multiset partitions.
  {{1,2,3,4}}        {{1,1,2,2}}        {{1,1,1,1}}
  {{1},{2,3,4}}      {{1},{1,2,2}}      {{1},{1,1,1}}
  {{1,2},{3,4}}      {{1,1},{2,2}}      {{1,1},{1,1}}
  {{1,3},{2,4}}      {{1,2},{1,2}}      {{1},{1},{1,1}}
  {{1,4},{2,3}}      {{2},{1,1,2}}      {{1},{1},{1},{1}}
  {{2},{1,3,4}}      {{1},{1},{2,2}}
  {{3},{1,2,4}}      {{1},{2},{1,2}}
  {{4},{1,2,3}}      {{2},{2},{1,1}}
  {{1},{2},{3,4}}    {{1},{1},{2},{2}}
  {{1},{3},{2,4}}
  {{1},{4},{2,3}}
  {{2},{3},{1,4}}
  {{2},{4},{1,3}}
  {{3},{4},{1,2}}
  {{1},{2},{3},{4}}

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

Row sums are A322784. First column is A000110.

Cf. A001055, A005176, A027750, A056239, A072774, A100778, A219727, A295193, A306017, A319190, A319612, A322784, A322785, A322787, A322788, A322792.

u[n_,k_]:=u[n,k]=If[n==1,1,Sum[u[n/d,d],{d,Select[Rest[Divisors[n]],#<=k&]}]];
Table[Table[u[Array[Prime,n/d,1,Times]^d,Array[Prime,n/d,1,Times]^d],{d,Divisors[n]}],{n,10}]

\\ needs T(n,k) from A219727.
Row(n)={[T(d,n/d) | d<-divisors(n)]}
{ for(n=1, 12, print(Row(n))) } \\ Andrew Howroyd, Jan 11 2020

T(n,k) = A001055(A002110(n/d)^d), where d = A027750(n,k).

T(n,k) = A219727(d, n/d), where d = A027750(n, k). - Andrew Howroyd, Jan 11 2020

Edited by Peter Munn, Mar 05 2025

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

A322833 Squarefree MM-numbers of strict uniform regular multiset multisystems. Squarefree numbers whose prime indices all have the same number of prime factors counted with multiplicity, and such that the product of the same prime indices is a power of a squarefree number.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 41, 43, 47, 51, 53, 55, 59, 67, 73, 79, 83, 85, 93, 97, 101, 103, 109, 113, 123, 127, 131, 137, 139, 149, 151, 155, 157, 161, 163, 165, 167, 177, 179, 181, 187, 191, 199, 201, 205, 211, 227, 233, 241, 249, 255

Offset: 1

Gus Wiseman, Dec 27 2018

nonn

A multiset multisystem is a finite multiset of finite multisets. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}.

A multiset multisystem is uniform if all parts have the same size, regular if all vertices appear the same number of times, and strict if there are no repeated parts. For example, {{1,2,2},{1,3,3}} is uniform, regular, and strict, so its MM-number 13969 belongs to the sequence. Note that the parts of parts such as {1,2,2} do not have to be distinct, only the multiset of parts.

			The sequence of all strict uniform regular multiset multisystems, together with their MM-numbers, begins:
   1: {}           59: {{7}}         157: {{12}}        269: {{2,8}}
   2: {{}}         67: {{8}}         161: {{1,1},{2,2}} 271: {{1,10}}
   3: {{1}}        73: {{2,4}}       163: {{1,8}}       277: {{17}}
   5: {{2}}        79: {{1,5}}       165: {{1},{2},{3}} 283: {{18}}
   7: {{1,1}}      83: {{9}}         167: {{2,6}}       293: {{1,11}}
  11: {{3}}        85: {{2},{4}}     177: {{1},{7}}     295: {{2},{7}}
  13: {{1,2}}      93: {{1},{5}}     179: {{13}}        311: {{1,1,1,1,1,1}}
  15: {{1},{2}}    97: {{3,3}}       181: {{1,2,4}}     313: {{3,6}}
  17: {{4}}       101: {{1,6}}       187: {{3},{4}}     317: {{1,2,5}}
  19: {{1,1,1}}   103: {{2,2,2}}     191: {{14}}        327: {{1},{10}}
  23: {{2,2}}     109: {{10}}        199: {{1,9}}       331: {{19}}
  29: {{1,3}}     113: {{1,2,3}}     201: {{1},{8}}     335: {{2},{8}}
  31: {{5}}       123: {{1},{6}}     205: {{2},{6}}     341: {{3},{5}}
  33: {{1},{3}}   127: {{11}}        211: {{15}}        347: {{2,9}}
  41: {{6}}       131: {{1,1,1,1,1}} 227: {{4,4}}       349: {{1,3,4}}
  43: {{1,4}}     137: {{2,5}}       233: {{2,7}}       353: {{20}}
  47: {{2,3}}     139: {{1,7}}       241: {{16}}        367: {{21}}
  51: {{1},{4}}   149: {{3,4}}       249: {{1},{9}}     373: {{1,12}}
  53: {{1,1,1,1}} 151: {{1,1,2,2}}   255: {{1},{2},{4}} 381: {{1},{11}}
  55: {{2},{3}}   155: {{2},{5}}     257: {{3,5}}       389: {{4,5}}

Cf. A005117, A007016, A112798, A302242, A306017, A319056, A319189, A320324, A321698, A321699, A322554, A322703.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],And[SquareFreeQ[#],SameQ@@PrimeOmega/@primeMS[#],SameQ@@Last/@FactorInteger[Times@@primeMS[#]]]&]

A323764 Dirichlet self-convolution of the integer partition numbers A000041.

Original entry on oeis.org

1, 1, 4, 6, 14, 14, 34, 30, 64, 69, 112, 112, 228, 202, 330, 394, 575, 594, 956, 980, 1492, 1674, 2228, 2510, 3700, 3965, 5276, 6200, 8126, 9130, 12318, 13684, 17842, 20622, 25808, 29976, 38377, 43274, 53990, 62976, 77912, 89166, 110656, 126522, 154918, 179744

Offset: 0

Gus Wiseman, Jan 27 2019

nonn

Also the number of multiset partitions of constant multiset partitions of integer partitions of n.

			The a(4) = 14 multiset partitions of constant multiset partitions:
  ((1111))              ((22))      ((4))  ((31))  ((211))
  ((11)(11))            ((2)(2))
  ((11))((11))          ((2))((2))
  ((1)(1)(1)(1))
  ((1))((1)(1)(1))
  ((1)(1))((1)(1))
  ((1))((1))((1)(1))
  ((1))((1))((1))((1))

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A000041, A000837, A001970, A002033, A003238, A034729, A047968, A279787, A305551, A306017, A319056, A323774.

Join[{1},Table[Sum[PartitionsP[d]*PartitionsP[n/d],{d,Divisors[n]}],{n,1,100}]]

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019

cp's OEIS Frontend

A301924 Regular triangle where T(n,k) is the number of unlabeled k-uniform connected hypergraphs spanning n vertices.

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A305552 Number of uniform normal multiset partitions of weight n.

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A306318 Number of square twice-partitions of n.

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A322531 Heinz numbers of integer partitions whose parts all have the same number of prime factors (counted with or without multiplicity) and whose product of parts is a squarefree number.

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A322703 Squarefree MM-numbers of strict uniform regular multiset systems spanning an initial interval of positive integers.

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A322786 Irregular triangle read by rows where T(n,k) is the number of multiset partitions of a multiset with d = A027750(n,k) copies of each integer from 1 to n/d.

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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.

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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.

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