OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..393
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-3*x^3/2 * exp(3*x))/3) = ( -2 * LambertW(-3*x^3/2 * exp(3*x))/(3*x^3) )^(1/3).
a(n) = n! * Sum_{k=0..floor(n/3)} (1/2)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3/2*exp(3*x))/3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 21 2023
STATUS
approved