A362673 E.g.f. satisfies A(x) = exp( x * exp(x^2) / A(x) ).

1, 1, -1, 10, -51, 556, -7085, 116376, -2263303, 51072400, -1308626649, 37526799520, -1190440709051, 41385630158016, -1564585725985477, 63903022429837696, -2804097015221308815, 131558782973452677376, -6571623885587502740657

Offset: 0

Author

Seiichi Manyama, Apr 29 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A362674.

Programs

PARI

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

Formula

E.g.f.: exp( LambertW(x * exp(x^2)) ).

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