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A341221 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^3.

%I A341221 #10 Feb 20 2021 05:47:07
%S A341221 1,6,21,59,144,321,669,1323,2511,4604,8202,14253,24241,40449,66363,
%T A341221 107234,170910,269004,418566,644436,982536,1484482,2223942,3305484,
%U A341221 4876620,7144455,10398123,15039564,21624678,30919323,43973708,62222844,87619212,122810585
%N A341221 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^3.
%H A341221 Alois P. Heinz, <a href="/A341221/b341221.txt">Table of n, a(n) for n = 3..10000</a>
%F A341221 a(n) ~ A000716(n). - _Vaclav Kotesovec_, Feb 20 2021
%p A341221 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
%p A341221       numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341221     end:
%p A341221 a:= n-> b(n, 3):
%p A341221 seq(a(n), n=3..36);  # _Alois P. Heinz_, Feb 07 2021
%t A341221 nmax = 36; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &
%Y A341221 Column k=3 of A060642.
%Y A341221 Cf. A000041, A000716, A048574, A327381, A341222, A341223, A341225, A341226, A341227, A341228.
%K A341221 nonn
%O A341221 3,2
%A A341221 _Ilya Gutkovskiy_, Feb 07 2021