A368537 a(n) = Sum_{k=1..n} binomial(k+2,3) * n^k.

0, 1, 18, 309, 5828, 123230, 2913126, 76405854, 2205340936, 69523722855, 2377899710410, 87721897714891, 3472488925101516, 146833416409808492, 6605726035373765678, 315051237815279406540, 15879038919798268666896, 843348814519524716426685

Offset

0,3

Links

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

Formula

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

a(n) = n * (n^n * (n^6-7*n^4+5*n^3+12*n^2-11*n-6) + 6)/(6 * (n-1)^4) for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, binomial(k+2, 3)*n^k);

Crossrefs

Cf. A062806, A368536.

Cf. A368527.

Sequence in context: A091045 A179121 A226298 * A321511 A208537 A292299

Adjacent sequences: A368534 A368535 A368536 * A368538 A368539 A368540

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2023

Status

approved