A362480 E.g.f. satisfies A(x) = exp(x - x^2 * A(x)^2).

1, 1, -1, -17, -47, 961, 14191, -35825, -4258463, -46744703, 1252890271, 49630926511, 61171154353, -41944148256191, -1033550755723121, 24977027757497551, 2117415434541888961, 20487158235798909697, -3240242006475108681665, -146763820123398901335185

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362481, A362482.

Cf. A143768, A362492.

Programs

PARI

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

Formula

E.g.f.: exp(x - LambertW(2*x^2 * exp(2*x))/2) = sqrt( LambertW(2*x^2 * exp(2*x))/(2*x^2) ).

a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (2*k+1)^(n-k-1) / (k! * (n-2*k)!).