A362352 a(n) = n! * Sum_{k=0..floor(n/4)} (k/24)^k / (k! * (n-4*k)!).

1, 1, 1, 1, 2, 6, 16, 36, 211, 1387, 6511, 23431, 225721, 2207921, 14610597, 71848141, 958259121, 12403693681, 105819536881, 659686502257, 11235532306021, 180826378073461, 1888306425160541, 14256573124903341, 295428115205647117, 5683724892725141901

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..494

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

Formula

E.g.f.: exp(x) / (1 + LambertW(-x^4/24)).

a(n) ~ (exp(2^(3/4)*3^(1/4)*exp(-1/4)) + (-1)^n/exp(2^(3/4)*3^(1/4)*exp(-1/4)) + 2*cos(2^(3/4)*3^(1/4)*exp(-1/4) - Pi*n/2)) * n^n / (2^(3*n/4 + 1) * 3^(n/4) * exp(3*n/4)). - Vaclav Kotesovec, Apr 18 2023

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^4/24))))

Crossrefs

Cf. A362350, A362351.

Cf. A362317.

Sequence in context: A351932 A329256 A128232 * A099099 A074082 A212383

Adjacent sequences: A362349 A362350 A362351 * A362353 A362354 A362355

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2023

Status

approved