A362350 a(n) = n! * Sum_{k=0..floor(n/2)} (k/2)^k / (k! * (n-2*k)!).
1, 1, 2, 4, 19, 71, 601, 3277, 39089, 277489, 4250341, 37110701, 693581197, 7184750509, 158461520309, 1899055549861, 48269252293201, 656869268651537, 18903165795857089, 287927838327392929, 9252988524143245181, 155954097639111859501
Offset: 0
Keywords
Links
- Winston de Greef, Table of n, a(n) for n = 0..437
- 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^2/2))))
Formula
E.g.f.: exp(x) / (1 + LambertW(-x^2/2)).
a(n) ~ (exp(2^(3/2)*exp(-1/2)) + (-1)^n) * n^n / (2^((n+1)/2) * exp(n/2 + sqrt(2)*exp(-1/2))). - Vaclav Kotesovec, Apr 18 2023