A361917 a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * (k+1)^(k-1) / (k! * (n-3*k)!).

1, 1, 1, -5, -23, -59, 961, 7351, 29905, -877463, -9450719, -52724429, 2282907001, 31742360365, 225092745697, -12992587010129, -221436656404319, -1905297800257199, 137972958868569025, 2784953660339878507, 28177036295775415561, -2459373614334806266859

Offset

0,4

Links

Table of n, a(n) for n=0..21.

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

Formula

E.g.f.: exp(x - LambertW(x^3)) = LambertW(x^3)/x^3 * exp(x).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^3))))

Crossrefs

Cf. A105785, A361916, A362523.

Sequence in context: A337750 A093622 A089137 * A362338 A098498 A159241

Adjacent sequences: A361914 A361915 A361916 * A361918 A361919 A361920

Keyword

sign,easy

Author

Seiichi Manyama, Apr 24 2023

Status

approved