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

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 A379613 A086946

Adjacent sequences: A368533 A368534 A368535 * A368537 A368538 A368539

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2023

Status

approved