A362522 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) / (k! * (n-2*k)!).

1, 1, 3, 7, 49, 201, 2491, 14743, 266337, 2055889, 49051891, 466650471, 13873711633, 156839920537, 5591748678699, 73222243463671, 3046762637864641, 45346835284775073, 2158148557098011107, 35980450963558606279, 1928292118820446611441

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..416

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: exp(x - LambertW(-x^2)) = -LambertW(-x^2)/x^2 * exp(x).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^2))))

Crossrefs

Cf. A088957, A362523.

Cf. A089461, A362347.

Sequence in context: A275830 A190444 A118393 * A113775 A113236 A035499

Adjacent sequences: A362519 A362520 A362521 * A362523 A362524 A362525

Keyword

nonn,easy,changed

Author

Seiichi Manyama, Apr 23 2023

Status

approved