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 A319066 Number of partitions of integer partitions of n where all parts have the same length. 30
 1, 1, 3, 5, 10, 14, 26, 35, 59, 82, 128, 176, 273, 371, 553, 768, 1119, 1544, 2235, 3084, 4410, 6111, 8649, 11982, 16901, 23383, 32780, 45396, 63365, 87622, 121946, 168407, 233605, 322269, 445723, 613922, 847131, 1164819, 1603431, 2201370, 3023660, 4144124, 5680816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 EXAMPLE The a(1) = 1 through a(5) = 14 multiset partitions:   {{1}}  {{2}}      {{3}}          {{4}}              {{5}}          {{1,1}}    {{1,2}}        {{1,3}}            {{1,4}}          {{1},{1}}  {{1,1,1}}      {{2,2}}            {{2,3}}                     {{1},{2}}      {{1,1,2}}          {{1,1,3}}                     {{1},{1},{1}}  {{1},{3}}          {{1,2,2}}                                    {{2},{2}}          {{1},{4}}                                    {{1,1,1,1}}        {{2},{3}}                                    {{1,1},{1,1}}      {{1,1,1,2}}                                    {{1},{1},{2}}      {{1,1,1,1,1}}                                    {{1},{1},{1},{1}}  {{1,1},{1,2}}                                                       {{1},{1},{3}}                                                       {{1},{2},{2}}                                                       {{1},{1},{1},{2}}                                                       {{1},{1},{1},{1},{1}} MATHEMATICA 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], SameQ@@Length/@#&]], {n, 8}] PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(p=1/prod(k=1, n, 1 - x^k*y + O(x*x^n))); concat([1], sum(k=1, n, EulerT(Vec(polcoef(p, k, y), -n))))} \\ Andrew Howroyd, Oct 25 2018 CROSSREFS Cf.  A001970, A047968, A261049, A279787, A305551, A306017, A319056. Sequence in context: A229915 A092269 A323429 * A306319 A182722 A089483 Adjacent sequences:  A319063 A319064 A319065 * A319067 A319068 A319069 KEYWORD nonn AUTHOR Gus Wiseman, Oct 10 2018 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Oct 25 2018 STATUS approved

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Last modified January 23 10:36 EST 2020. Contains 331171 sequences. (Running on oeis4.)