A362317 a(n) = n! * Sum_{k=0..floor(n/4)} (n/24)^k /(k! * (n-4*k)!).

1, 1, 1, 1, 5, 26, 91, 246, 2801, 26650, 159601, 702406, 12479941, 172561676, 1462655195, 8918930476, 215370384321, 3906667179836, 42828875064001, 333816101642140, 10190496077676901, 228789539391769336, 3077152545301687931, 29203537040556576776

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..465

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

Formula

a(n) = n! * [x^n] exp(x + n*x^4/24).

E.g.f.: exp( ( -6*LambertW(-x^4/6) )^(1/4) ) / (1 + LambertW(-x^4/6)).

Mathematica

nmax = 30; CoefficientList[PowerExpand[Series[E^((-6*LambertW[-x^4/6])^(1/4)) / (1 + LambertW[-x^4/6]), {x, 0, nmax}]], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 18 2023 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-6*lambertw(-x^4/6))^(1/4))/(1+lambertw(-x^4/6))))

Crossrefs

Cf. A362173, A362336.

Cf. A351932, A362314.

Sequence in context: A079909 A301518 A350406 * A047669 A297689 A002316

Adjacent sequences: A362314 A362315 A362316 * A362318 A362319 A362320

Keyword

nonn

Author

Seiichi Manyama, Apr 16 2023

Status

approved