A362350 a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)^k / (k! * (n-2*k)!).

1, 1, 2, 4, 19, 71, 601, 3277, 39089, 277489, 4250341, 37110701, 693581197, 7184750509, 158461520309, 1899055549861, 48269252293201, 656869268651537, 18903165795857089, 287927838327392929, 9252988524143245181, 155954097639111859501

Offset

0,3

Links

Winston de Greef, Table of n, a(n) for n = 0..437

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

Formula

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

a(n) ~ (exp(2^(3/2)*exp(-1/2)) + (-1)^n) * n^n / (2^((n+1)/2) * exp(n/2 + sqrt(2)*exp(-1/2))). - Vaclav Kotesovec, Apr 18 2023

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2/2))))

Crossrefs

Cf. A362351, A362352.

Cf. A277614.

Sequence in context: A229485 A064228 A226891 * A289269 A363303 A272988

Adjacent sequences: A362347 A362348 A362349 * A362351 A362352 A362353

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2023

Status

approved