A362281 a(n) = n! * Sum_{k=0..floor(n/2)} n^k * binomial(n-k,k)/(n-k)!.

1, 1, 5, 19, 241, 1601, 32581, 308995, 8655809, 106673761, 3805452901, 57704760851, 2500580809585, 45018720191329, 2295683481085541, 47848514992963651, 2806491306922172161, 66464103165835330625, 4407449313521981148229, 116893033842508769526931

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..395

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

Formula

a(n) = n! * [x^n] exp(x + n*x^2).

E.g.f.: exp( sqrt( -LambertW(-2*x^2)/2 ) ) / (1 + LambertW(-2*x^2)).

a(n) ~ (1 + (-1)^n/exp(sqrt(2))) * 2^((n-1)/2) * n^n / exp(n/2 - 1/sqrt(2)). - Vaclav Kotesovec, Apr 15 2023

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sqrt(-lambertw(-2*x^2)/2))/(1+lambertw(-2*x^2))))

Crossrefs

Cf. A277614, A362282.

Sequence in context: A317340 A328716 A067967 * A092751 A357363 A122150

Adjacent sequences: A362278 A362279 A362280 * A362282 A362283 A362284

Keyword

nonn

Author

Seiichi Manyama, Apr 14 2023

Status

approved