A368527 a(n) = Sum_{k=1..n} k^3 * n^k.

0, 1, 34, 804, 18244, 434205, 11138766, 310151632, 9370253320, 306232628625, 10783859167810, 407523041660196, 16461877678462668, 708207095198943613, 32338800248010936694, 1562509380160144645440, 79657105206246202521616

Offset

0,3

Links

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

Formula

a(n) = [x^n] n*x * (1+4*n*x+(n*x)^2)/((1-x) * (1-n*x)^4).

a(n) = n * (n^n * (n^6-3*n^5+8*n^3-4*n^2-7*n-1) + n^2 + 4*n + 1)/(n-1)^4 for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, k^3*n^k);

Crossrefs

Cf. A062806, A303991, A368526.

Cf. A368525.

Sequence in context: A160315 A078193 A063843 * A192094 A297337 A295351

Adjacent sequences: A368524 A368525 A368526 * A368528 A368529 A368530

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 28 2023

Status

approved