OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (LambertW( -3*x^2/(1-x)^3 ) / (-3*x^2))^(1/3).
a(n) = n! * Sum_{k=0..floor(n/2)} (3*k+1)^(k-1) * binomial(n+k,n-2*k)/k!.
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x^2/(1-x)^3)/(-3*x^2))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*binomial(n+k, n-2*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved