A368536 - OEIS

A368536

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

0, 1, 14, 192, 2996, 53955, 1110786, 25808160, 668740808, 19129643325, 598902606310, 20371538593296, 748148581865532, 29505258575474591, 1243695052515891626, 55800352470853933440, 2655106829377875895056, 133547801741230053460761

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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)^3).

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

PROG

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

CROSSREFS

Cf. A062806, A368537.

Cf. A368526.

Sequence in context: A198657 A055759 A368702 * A275084 A086946 A158530

Adjacent sequences: A368533 A368534 A368535 * A368537 A368538 A368539

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Dec 29 2023

STATUS

approved