A368534 a(n) = Sum_{k=1..n} binomial(k+1,2) * n^(n-k).

0, 1, 5, 24, 146, 1215, 13431, 186816, 3130436, 61291125, 1371742105, 34522712136, 964626945558, 29621465864627, 991330604373851, 35906022352657920, 1399219698628043016, 58367293868445147657, 2594796705962971336125, 122463905297217627859000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

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

Mathematica

Table[Sum[Binomial[k+1, 2]n^(n-k), {k, n}], {n, 0, 20}] (* Harvey P. Dale, May 14 2025 *)

Prog

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

Crossrefs

Cf. A062805, A368535.

Cf. A002662, A052150, A052161.

Cf. A023037, A062806, A068475.

Sequence in context: A201952 A221788 A111766 * A228067 A372138 A322208

Adjacent sequences: A368531 A368532 A368533 * A368535 A368536 A368537

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2023

Status

approved