OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (1+x)^2 * exp( -LambertW(-x*(1+x)^2) ).
E.g.f.: -LambertW(-x*(1+x)^2)/x.
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(2*k+2,n-k)/k!.
a(n) ~ sqrt(1 + 3*r) * n^(n-1) / (exp(n - 1/4) * r^(n + 3/4)), where r = 0.2394629861788505554394435808448... is root of the equation r*(1+r)^2 = exp(-1). - Vaclav Kotesovec, Nov 09 2024
PROG
(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(2*k+2, n-k)/k!);
CROSSREFS
KEYWORD
nonn,new
AUTHOR
Seiichi Manyama, Nov 09 2024
STATUS
approved