A368526 a(n) = Sum_{k=1..n} k^2 * n^k.

0, 1, 18, 282, 4740, 89355, 1896846, 45050852, 1186829064, 34391135205, 1087928669410, 37322190255966, 1380461544684300, 54772368958008975, 2320775754168090870, 104596636848116060040, 4996700995031905899536, 252208510175779038669321

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = [x^n] n*x * (1+n*x)/((1-x) * (1-n*x)^3).

a(n) = n * (n+1) * (n^n * (n^3-3*n^2+2*n+1) - 1)/(n-1)^3 for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, k^2*n^k);

Crossrefs

Cf. A062806, A303991, A368527.

Cf. A368524.

Sequence in context: A004357 A249598 A245924 * A035119 A230235 A288959

Adjacent sequences: A368523 A368524 A368525 * A368527 A368528 A368529

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 28 2023

Status

approved