A361617 a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*(k+1),n-k)/k!.

1, 2, 15, 214, 4721, 146046, 5958367, 307382090, 19459587009, 1478414285146, 132440451881231, 13787717744245182, 1647673524863409265, 223671725058601427414, 34184743554559413628191, 5837132027535188545269106, 1106136052471647285563082497

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..272

Formula

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

a(n) = Sum_{k=0..n} (n+(n-1)*(k+1))!/(n*k+n-1)! * binomial(n,k) for n > 0.

Prog

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

Crossrefs

Main diagonal of A361616.

Cf. A361607.

Sequence in context: A099718 A143881 A298692 * A132493 A135860 A178533

Adjacent sequences: A361614 A361615 A361616 * A361618 A361619 A361620

Keyword

nonn

Author

Seiichi Manyama, Mar 18 2023

Status

approved