OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: A(x) = exp( 2*x - 2*LambertW(-x^3 * exp(x)) ).
a(n) = 2 * n! * Sum_{k=0..floor(n/3)} (k+2)^(n-2*k-1) / (k! * (n-3*k)!).
a(n) ~ 2*sqrt(1 + LambertW(exp(-1/3)/3)) * n^(n-1) / (3^(n + 11/2) * exp(n) * LambertW(exp(-1/3)/3)^(n+6)). - Vaclav Kotesovec, Jun 01 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*x-2*lambertw(-x^3*exp(x)))))
(PARI) a(n) = 2*n!*sum(k=0, n\3, (k+2)^(n-2*k-1)/(k!*(n-3*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 23 2024
STATUS
approved