A361916 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (k+1)^(k-1) / (k! * (n-2*k)!).
1, 1, -1, -5, 25, 161, -1409, -12221, 158705, 1733185, -30136769, -397326709, 8696945929, 134416055905, -3555479651905, -63044502191789, 1957884163020001, 39178556553643649, -1398250387206450305, -31169265056007817445, 1257498026543130033401
Offset: 0
Links
- 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).