A362571 E.g.f. satisfies A(x) = exp(x * A(x)^(x^2)).

1, 1, 1, 1, 25, 121, 361, 8401, 82321, 456625, 11496241, 172149121, 1452983401, 40947003241, 823437038425, 9491714865361, 300842942443681, 7568303382376801, 111494036396244961, 3957438528527140225, 119206427681076135481, 2147109997071581380441

Offset: 0

Author

Seiichi Manyama, Apr 25 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..427
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A000272, A361777.

Cf. A362569, A362573.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^3)))))

Formula

E.g.f.: (-LambertW(-x^3) / x^3)^(1/x^2) = exp(-LambertW(-x^3) / x^2) = exp(x * exp(-LambertW(-x^3))).

a(n) = n! * Sum_{k=0..floor(n/3)} (n-2*k)^k * binomial(n-2*k-1,k)/(n-2*k)!.

E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * x^k / k!.