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

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Lambert W-Function.

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/2-lambertw(-x*exp(x^2/2)))))

Crossrefs

Cf. A349562, A362748.

Cf. A143740, A362690.

Sequence in context: A259842 A125863 A004115 * A222885 A235329 A220231

Adjacent sequences: A362744 A362745 A362746 * A362748 A362749 A362750

Keyword

nonn

Author

Seiichi Manyama, May 02 2023

Status

approved