A349854 Expansion of Sum_{k>=0} k^3 * x^k/(1 + k * x).

0, 1, 7, 12, 14, 49, 13, 8, 596, -1967, 4011, 9764, -128878, 664545, -1837695, -2388448, 67004968, -478198239, 1994890287, -1669470404, -56929813514, 615188040657, -3794477505067, 12028579020088, 50780206473820, -1172949397923535, 10766410530764819, -61183127006113196

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Crossrefs

Cf. A038125, A349852, A349853, A349855.

Programs

Mathematica

a[n_] := -Sum[(-k)^(n - k + 3), {k, 0, n}]; Array[a, 28, 0] (* Amiram Eldar, Dec 02 2021 *)

PARI

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

PARI

my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, k^3*x^k/(1+k*x))))

Formula

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