A362305 a(n) = n! * Sum_{k=0..floor(n/3)} (-n)^k * binomial(n-2*k,k)/(n-2*k)!.

1, 1, 1, -17, -95, -299, 12241, 122011, 642433, -41645015, -597247199, -4407324569, 390913189921, 7315513279933, 69439658097265, -7816418805235949, -180448412456686079, -2093964182367814319, 285679499679525805633, 7844019340520912230495

Offset

0,4

Links

Winston de Greef, Table of n, a(n) for n = 0..402

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

Formula

a(n) = A362302(n,6*n).

a(n) = n! * [x^n] exp(x - n*x^3).

E.g.f.: exp( ( LambertW(3*x^3)/3 )^(1/3) ) / (1 + LambertW(3*x^3)).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((lambertw(3*x^3)/3)^(1/3))/(1+lambertw(3*x^3))))

Crossrefs

Cf. A362301, A362302.

Sequence in context: A253259 A119783 A199042 * A264211 A094407 A131204

Adjacent sequences: A362302 A362303 A362304 * A362306 A362307 A362308

Keyword

sign

Author

Seiichi Manyama, Apr 15 2023

Status

approved