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A341223 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^5.

%I A341223 #8 Feb 07 2021 11:52:06
%S A341223 1,10,55,225,765,2287,6215,15680,37265,84300,182933,383070,777705,
%T A341223 1536490,2963120,5592060,10349465,18817760,33665870,59341785,
%U A341223 103176877,177131330,300530125,504318530,837632700,1377874861,2246061540,3630059510,5819556060,9258393655,14622472250
%N A341223 Expansion of (-1 + Product_{k>=1} 1 / (1 - x^k))^5.
%H A341223 Alois P. Heinz, <a href="/A341223/b341223.txt">Table of n, a(n) for n = 5..10000</a>
%p A341223 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, combinat[
%p A341223       numbpart](n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341223     end:
%p A341223 a:= n-> b(n, 5):
%p A341223 seq(a(n), n=5..35);  # _Alois P. Heinz_, Feb 07 2021
%t A341223 nmax = 35; CoefficientList[Series[(-1 + Product[1/(1 - x^k), {k, 1, nmax}])^5, {x, 0, nmax}], x] // Drop[#, 5] &
%Y A341223 Column k=5 of A060642.
%Y A341223 Cf. A000041, A023004, A048574, A327383, A341221, A341222, A341225, A341226, A341227, A341228.
%K A341223 nonn
%O A341223 5,2
%A A341223 _Ilya Gutkovskiy_, Feb 07 2021