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%I #13 Sep 07 2018 12:04:09
%S 1,1,3,4,9,8,22,16,43,41,77,57,201,102,264,282,564,298,1175,491,1878,
%T 1509,2611,1256,7872,2421,7602,8026,16304,4566,38434,6843,48308,41078,
%U 56582,28228,221115,21638,146331,208142,453017,44584,844773,63262,1034193,1296708
%N Number of partitions of partitions of n where all partitions have the same sum.
%H Andrew Howroyd, <a href="/A305551/b305551.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{d|n} binomial(A000041(n/d) + d - 1, d).
%e The a(4) = 9 partitions of partitions where all partitions have the same sum:
%e (4), (31), (22), (211), (1111),
%e (2)(2), (2)(11), (11)(11),
%e (1)(1)(1)(1).
%t Table[Sum[Binomial[PartitionsP[n/k]+k-1,k],{k,Divisors[n]}],{n,60}]
%o (PARI) a(n)={if(n<1, n==0, sumdiv(n, d, binomial(numbpart(n/d) + d - 1, d)))} \\ _Andrew Howroyd_, Jun 22 2018
%Y Cf. A000005, A001970, A001315, A007716, A038041, A055887, A063834, A271619, A289078, A298422, A306017.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jun 20 2018