%I #20 Dec 11 2021 04:29:30
%S 1,1,0,-6,37,155,-11616,251940,783641,-454238419,29895012768,
%T -757531311386,-106105977022243,21452688824818775,
%U -2105573104903303616,16702280440994303008,48278492787774402969521,-13301912828187822051695559,1964564462643243537548661568
%N Expansion of Sum_{k>=0} x^k/(1 + k^3 * x).
%H Seiichi Manyama, <a href="/A349857/b349857.txt">Table of n, a(n) for n = 0..247</a>
%F a(n) = Sum_{k=0..n} (-k^3)^(n-k).
%t a[n_] := Sum[If[k == n - k == 0, 1, (-k^3)^(n-k)], {k, 0, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Dec 03 2021 *)
%o (PARI) a(n, s=0, t=3) = sum(k=0, n, (-k^t)^(n-k)*k^s);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^3*x)))
%Y Cf. A349856, A349858, A349902.
%K sign
%O 0,4
%A _Seiichi Manyama_, Dec 02 2021