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

0,4

Links

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

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

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)!).

a(n) ~ -(-1)^n * exp(-1) * sqrt(1 + LambertW(2*exp(-2))) * 2^(n/2) * n^(n-1) / (exp(n) * LambertW(2*exp(-2))^(n/2)). - Vaclav Kotesovec, Jan 29 2026

Prog

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

Crossrefs

Cf. A362674.

Sequence in context: A224327 A219573 A135242 * A041186 A058827 A232909

Adjacent sequences: A362670 A362671 A362672 * A362674 A362675 A362676

Keyword

sign

Author

Seiichi Manyama, Apr 29 2023

Status

approved