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