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%I #5 May 09 2021 11:17:06
%S 1,1,6,27,92,323,1070,3527,11314,35708,110478,336629,1011097,2997233,
%T 8778761,25424358,72867447,206804742,581573340,1621407554,4483701126,
%U 12303384015,33514076529,90656680725,243603875523,650444927010,1726229294595,4554686670838,11950683658941
%N Expansion of Product_{k>=1} (1 + x^k)^binomial(k+4,5).
%F G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^6) ).
%t nmax = 28; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 4, 5], {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, 5], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 28}]
%Y Cf. A000389, A000417, A028377, A258343, A305206, A344099, A344101.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 09 2021