A368488 a(n) = Sum_{k=0..n} n^k * binomial(k+n-1,k).

1, 2, 17, 334, 10417, 442276, 23690809, 1530206742, 115636017473, 10004657077468, 974950612575601, 105653682110368492, 12602144701834193521, 1640558582759557298696, 231448351542446473323113, 35173958220088874039434726, 5728588740444710703061240065

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

a(n) ~ 2^(2*n-1) * n^(n - 1/2) / sqrt(Pi). - Vaclav Kotesovec, Dec 27 2023

Prog

(PARI) a(n) = sum(k=0, n, n^k*binomial(k+n-1, k));

Crossrefs

Main diagonal of A368487.

Cf. A000984, A072547.

Sequence in context: A007785 A360609 A201785 * A204249 A242368 A307315

Adjacent sequences: A368485 A368486 A368487 * A368489 A368490 A368491

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 26 2023

Status

approved