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A349885 Expansion of Sum_{k>=0} (k * x)^k/(1 + k^3 * x). 2
1, 1, 3, -4, -218, 4377, 189549, -13317056, -283835940, 117015022505, -5604964950389, -1791024716075124, 422751913131376674, 8850160172208790801, -30082452518043880807911, 7173002090013176579439392, 1556433498641034120823054072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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

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 *)

PROG

(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)))

CROSSREFS

Cf. A120485, A349884.

Sequence in context: A245456 A042275 A012861 * A042485 A111315 A042711

Adjacent sequences:  A349882 A349883 A349884 * A349886 A349887 A349888

KEYWORD

sign

AUTHOR

Seiichi Manyama, Dec 03 2021

STATUS

approved

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Last modified August 18 18:56 EDT 2022. Contains 356215 sequences. (Running on oeis4.)