A349853 Expansion of Sum_{k>=0} k^2 * x^k/(1 + k * x).

0, 1, 3, 2, 4, 11, -13, 36, 56, -515, 2067, -3890, -9620, 129047, -664349, 1837920, 2388704, -67004679, 478198563, -1994889926, 1669470804, 56929813955, -615188040173, 3794477505596, -12028579019512, -50780206473195, 1172949397924211, -10766410530764090

Offset: 0

Author

Seiichi Manyama, Dec 02 2021

Keywords

• sign

Crossrefs

Cf. A038125, A349852, A349854, A349855.

Programs

Mathematica

a[n_] := Sum[(-k)^(n - k + 2), {k, 0, n}]; Array[a, 28, 0] (* Amiram Eldar, Dec 02 2021 *)

PARI

a(n, s=2, 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^2*x^k/(1+k*x))))

Formula

a(n) = Sum_{k=0..n} (-k)^(n-k+2).