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%I #5 May 09 2021 11:16:47
%S 1,5,25,120,505,2027,7740,28345,100355,344815,1154130,3773955,
%T 12085125,37971645,117258755,356386016,1067364240,3153415695,
%U 9198749905,26516197720,75586609016,213212467695,595482274750,1647568369230,4517987288720,12284672226583,33133931688645
%N Expansion of Product_{k>=1} (1 + x^k)^binomial(k+4,4).
%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * A174002(d) ) * a(n-k).
%t nmax = 26; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 4, 4], {k, 1, nmax}], {x, 0, nmax}], x]
%t a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[(-1)^(k/d + 1) d Binomial[d + 4, 4], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 26}]
%Y Cf. A000332, A174002, A219555, A255052, A338645, A343200, A344098.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, May 09 2021
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