cp's OEIS Frontend

A341391 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^8.

%I A341391 #8 Feb 10 2021 18:56:26
%S A341391 1,16,152,1072,6204,31024,138544,564824,2135902,7580944,25485560,
%T A341391 81734696,251514840,746123304,2142114356,5971477112,16208165181,
%U A341391 42936937488,111240873128,282363615336,703303327288,1721329848680,4144792701532,9829483710112
%N A341391 Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^8.
%H A341391 Alois P. Heinz, <a href="/A341391/b341391.txt">Table of n, a(n) for n = 8..10000</a>
%p A341391 g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/
%p A341391      `if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)
%p A341391     end:
%p A341391 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
%p A341391       g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A341391     end:
%p A341391 a:= n-> b(n, 8):
%p A341391 seq(a(n), n=8..31);  # _Alois P. Heinz_, Feb 10 2021
%t A341391 nmax = 31; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^8, {x, 0, nmax}], x] // Drop[#, 8] &
%Y A341391 Cf. A026007, A321953, A327386, A341384, A341385, A341386, A341387, A341388, A341390.
%K A341391 nonn
%O A341391 8,2
%A A341391 _Ilya Gutkovskiy_, Feb 10 2021