cp's OEIS Frontend

A341247 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^8.

%I A341247 #6 Feb 07 2021 14:00:20
%S A341247 1,0,8,8,36,64,148,296,562,1080,1920,3440,5890,9992,16532,26920,43175,
%T A341247 68144,106260,163472,248824,374504,558212,824208,1206409,1751360,
%U A341247 2522692,3607456,5122848,7227392,10132948,14123000,19573393,26981768,37003700,50499952,68595956
%N A341247 Expansion of (-1 + Product_{k>=1} 1 / (1 + (-x)^k))^8.
%F A341247 G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^8.
%p A341247 g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
%p A341247       [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
%p A341247     end:
%p A341247 b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
%p A341247       (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
%p A341247     end:
%p A341247 a:= n-> b(n, 8):
%p A341247 seq(a(n), n=8..44);  # _Alois P. Heinz_, Feb 07 2021
%t A341247 nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &
%Y A341247 Cf. A000700, A001486, A007259, A101127, A327386, A338463, A341227, A341241, A341243, A341244, A341245, A341246, A341251.
%K A341247 nonn
%O A341247 8,3
%A A341247 _Ilya Gutkovskiy_, Feb 07 2021