OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: LambertW( -x^3/(1-x) ) / (-x^3).
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n-2*k,n-3*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(-x^3/(1-x))/(-x^3)))
(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k, n-3*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved