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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..465
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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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 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-6*lambertw(-x^4/6))^(1/4))/(1+lambertw(-x^4/6))))
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)).