A349885 Expansion of Sum_{k>=0} (k * x)^k/(1 + k^3 * x).

1, 1, 3, -4, -218, 4377, 189549, -13317056, -283835940, 117015022505, -5604964950389, -1791024716075124, 422751913131376674, 8850160172208790801, -30082452518043880807911, 7173002090013176579439392, 1556433498641034120823054072

Offset: 0

Author

Seiichi Manyama, Dec 03 2021

Keywords

• sign

Crossrefs

Cf. A120485, A349884.

Programs

Mathematica

a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, (-1)^(n - k) * k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 04 2021 *)

PARI

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

PARI

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n-2*k).