A362736 E.g.f. satisfies A(x) = exp(x^2 + x / A(x)).

1, 1, 1, 4, -3, 96, -755, 10368, -147623, 2492416, -47137959, 996741120, -23260103339, 594198429696, -16492683271259, 494278721929216, -15908038836914895, 547238863907586048, -20038031401448021327, 778147549666716155904, -31943565308583934360019

Offset

0,4

Links

Table of n, a(n) for n=0..20.

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

Formula

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

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

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2+lambertw(x*exp(-x^2)))))

Crossrefs

Cf. A362693, A362737.

Cf. A362690.

Sequence in context: A299188 A300026 A349589 * A266255 A351792 A362674

Adjacent sequences: A362733 A362734 A362735 * A362737 A362738 A362739

Keyword

sign

Author

Seiichi Manyama, May 01 2023

Status

approved