OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp( -LambertW(-3*x^3 * (1+x))/3 ).
a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(k,n-3*k)/k!.
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x^3*(1+x))/3)))
(PARI) a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(k, n-3*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 25 2024
STATUS
approved