A360601 E.g.f. satisfies A(x) = exp(x*A(x)^2) / (1-x).
1, 2, 13, 166, 3265, 87306, 2957509, 121400350, 5857287937, 324884241874, 20370279663901, 1424790170536470, 109990236302275201, 9289460282062082266, 852049115732672006101, 84345608594930495005966, 8962937531710834906989313, 1017655033307013508626619554
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x/(1-x)^2)/(-2*x))))
Formula
E.g.f.: sqrt(LambertW( -2*x/(1-x)^2 ) / (-2*x)).
a(n) ~ sqrt(1 + 2*exp(-1) - sqrt(1 + 2*exp(-1))) * n^(n-1) / (2 * (sqrt(1 + 2*exp(-1)) - 1)^(3/2) * exp(2*n + 1/2) * (1 + exp(-1) - sqrt(1 + 2*exp(-1)))^n). - Vaclav Kotesovec, Mar 06 2023
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n+k,n-k)/k!. - Seiichi Manyama, Mar 09 2024