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%I #14 Dec 05 2020 14:42:58
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4,6,8,12,16,23,31,43,57,78,102,
%T 136,177,232,297,384,487,621,781,984,1226,1531,1892,2340,2872,3524,
%U 4294,5232,6335,7666,9229,11099,13288,15893,18929,22519,26695,31604,37293
%N G.f.: Sum_{k>=0} x^(k^4) / Product_{j=1..k^4} (1 - x^j).
%C Number of partitions of n such that the number of parts is a fourth power.
%C Also number of partitions of n such that the largest part is a fourth power.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(18) = 3 because we have [18], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the first comment) or[16, 2], [16, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the second comment).
%t nmax = 57; CoefficientList[Series[Sum[x^(k^4)/Product[1 - x^j, {j, 1, k^4}], {k, 0, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x]
%Y Cf. A000583, A046042, A089333, A334626.
%K nonn
%O 0,17
%A _Ilya Gutkovskiy_, Dec 05 2020
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