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A341387 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^5.

%I A341387 #9 Feb 10 2021 18:22:42
%S A341387 1,10,65,320,1330,4872,16255,50335,146775,407045,1082000,2773045,
%T A341387 6884650,16620225,39135280,90113553,203347645,450516450,981491380,
%U A341387 2105504205,4452798556,9293254605,19158353285,39044262235,78719105560,157112112293,310599279105
%N A341387 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^5.
%H A341387 Alois P. Heinz, <a href="/A341387/b341387.txt">Table of n, a(n) for n = 5..10000</a>
%p A341387 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341387      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341387     end:
%p A341387 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341387       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341387     end:
%p A341387 a:= n-> b(n, 5):
%p A341387 seq(a(n), n=5..31);  # _Alois P. Heinz_, Feb 10 2021
%t A341387 nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341387 Cf. A026007, A321950, A327383, A341384, A341385, A341386, A341388, A341390, A341391.
%K A341387 nonn
%O A341387 5,2
%A A341387 _Ilya Gutkovskiy_, Feb 10 2021