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%I #16 Oct 26 2018 00:51:59
%S 1,1,3,5,10,14,26,35,59,82,128,176,273,371,553,768,1119,1544,2235,
%T 3084,4410,6111,8649,11982,16901,23383,32780,45396,63365,87622,121946,
%U 168407,233605,322269,445723,613922,847131,1164819,1603431,2201370,3023660,4144124,5680816
%N Number of partitions of integer partitions of n where all parts have the same length.
%H Andrew Howroyd, <a href="/A319066/b319066.txt">Table of n, a(n) for n = 0..500</a>
%e The a(1) = 1 through a(5) = 14 multiset partitions:
%e {{1}} {{2}} {{3}} {{4}} {{5}}
%e {{1,1}} {{1,2}} {{1,3}} {{1,4}}
%e {{1},{1}} {{1,1,1}} {{2,2}} {{2,3}}
%e {{1},{2}} {{1,1,2}} {{1,1,3}}
%e {{1},{1},{1}} {{1},{3}} {{1,2,2}}
%e {{2},{2}} {{1},{4}}
%e {{1,1,1,1}} {{2},{3}}
%e {{1,1},{1,1}} {{1,1,1,2}}
%e {{1},{1},{2}} {{1,1,1,1,1}}
%e {{1},{1},{1},{1}} {{1,1},{1,2}}
%e {{1},{1},{3}}
%e {{1},{2},{2}}
%e {{1},{1},{1},{2}}
%e {{1},{1},{1},{1},{1}}
%t sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t Table[Length[Select[Join@@mps/@IntegerPartitions[n],SameQ@@Length/@#&]],{n,8}]
%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o 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
%Y Cf. A001970, A047968, A261049, A279787, A305551, A306017, A319056.
%K nonn
%O 0,3
%A _Gus Wiseman_, Oct 10 2018
%E Terms a(11) and beyond from _Andrew Howroyd_, Oct 25 2018
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