A362347 a(n) = n! * Sum_{k=0..floor(n/2)} k^k / (k! * (n-2*k)!).
1, 1, 3, 7, 61, 261, 3991, 24403, 524217, 4149001, 114544171, 1111976031, 37492210933, 431097055117, 17165526306111, 228085258466731, 10472666396599921, 157882659583461393, 8211536252680154707, 138474928851961700791, 8045878340298511456941
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..414
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^2))))
Formula
E.g.f.: exp(x) / (1 + LambertW(-x^2)).
a(n) ~ (exp(2*exp(-1/2)) + (-1)^n) * n^n / (sqrt(2) * exp(n/2 + exp(-1/2))). - Vaclav Kotesovec, Aug 05 2025