A349860 Expansion of Sum_{k>=0} k * x^k/(1 + k^3 * x).

0, 1, 1, -12, 50, 913, -35093, 557048, 15098348, -1975843727, 103722820509, -396969408196, -704487440688562, 106081534307130081, -7995154887120369801, -510404434212739199104, 340061796037700870259064, -75820293495741408235957599, 8142099722101269515604494937

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Crossrefs

Cf. A349859, A349861.

Programs

Mathematica

a[n_] := Sum[If[k == n - k == 0, 1, (-k^3)^(n-k)] * k, {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 03 2021 *)

PARI

a(n, s=1, t=3) = sum(k=0, n, (-k^t)^(n-k)*k^s);

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k*x^k/(1+k^3*x))))

Formula

a(n) = Sum_{k=0..n} (-k^3)^(n-k) * k.