A362522 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) / (k! * (n-2*k)!).
1, 1, 3, 7, 49, 201, 2491, 14743, 266337, 2055889, 49051891, 466650471, 13873711633, 156839920537, 5591748678699, 73222243463671, 3046762637864641, 45346835284775073, 2158148557098011107, 35980450963558606279, 1928292118820446611441
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..416
- 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-lambertw(-x^2))))
Formula
E.g.f.: exp(x - LambertW(-x^2)) = -LambertW(-x^2)/x^2 * exp(x).
a(n) ~ sqrt(2) * (exp(2*exp(-1/2)) + (-1)^n) * n^(n-1) / exp(n/2 + exp(-1/2) - 1). - Vaclav Kotesovec, Aug 05 2025