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A341222 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^4.

%I A341222 #10 Feb 20 2021 05:47:39
%S A341222 1,8,36,124,362,944,2266,5100,10903,22340,44168,84692,158137,288452,
%T A341222 515344,903740,1558465,2646820,4432964,7329916,11977507,19358524,
%U A341222 30970444,49077936,77081679,120054268,185514428,284540060,433360308,655622392,985604644,1472751228
%N A341222 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^4.
%H A341222 Alois P. Heinz, <a href="/A341222/b341222.txt">Table of n, a(n) for n = 4..10000</a>
%F A341222 a(n) ~ A023003(n). - _Vaclav Kotesovec_, Feb 20 2021
%p A341222 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
%p A341222       numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341222     end:
%p A341222 a:= n-> b(n, 4):
%p A341222 seq(a(n), n=4..35);  # _Alois P. Heinz_, Feb 07 2021
%t A341222 nmax = 35; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^4, {x, 0, nmax}], x] // Drop[#, 4] &
%Y A341222 Column k=4 of A060642.
%Y A341222 Cf. A000041, A023003, A048574, A327382, A341221, A341223, A341225, A341226, A341227, A341228.
%K A341222 nonn
%O A341222 4,2
%A A341222 _Ilya Gutkovskiy_, Feb 07 2021