A361917 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.