A368510 a(n) = Sum_{k=0..n} n^(n-k) * binomial(k+n,k).

1, 3, 16, 113, 1026, 11782, 166776, 2825349, 55797790, 1258065866, 31866312336, 895430095738, 27632885411236, 928823226029532, 33772464199743184, 1320627875038128045, 55259636489069057910, 2463499964955575965954, 116560977980742613228704

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Dec 28 2023

Prog

(PARI) a(n) = sum(k=0, n, n^(n-k)*binomial(n+k, k));

Crossrefs

Cf. A293574, A368489.

Sequence in context: A124537 A355720 A305133 * A074523 A329113 A042437

Adjacent sequences: A368507 A368508 A368509 * A368511 A368512 A368513

Keyword

nonn

Author

Seiichi Manyama, Dec 28 2023

Status

approved