A362747 E.g.f. satisfies A(x) = exp(x^2/2 + x * A(x)).
1, 1, 4, 22, 182, 1996, 27412, 453160, 8767516, 194438800, 4864250096, 135538060384, 4163356010728, 139784741268160, 5093269640966704, 200170986137297536, 8440841773833141008, 380153135554220691712, 18212499110682362677312
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Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/2-lambertw(-x*exp(x^2/2)))))
Formula
E.g.f.: -LambertW(-x * exp(x^2/2)) / x = exp( x^2/2 - LambertW(-x*exp(x^2/2)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)^(n-k-1) / (2^k * k! * (n-2*k)!).
a(n) ~ sqrt(1+LambertW(exp(-2))) * n^(n-1) / (exp(n)*LambertW(exp(-2))^((n+1)/2)). - Vaclav Kotesovec, Nov 10 2023