A362391 E.g.f. satisfies A(x) = exp(x + x^3/2 * A(x)).

1, 1, 1, 4, 25, 121, 751, 7351, 73417, 749449, 9477181, 136883341, 2041250641, 33289802833, 608025141907, 11815916748091, 242532915013201, 5369303859003601, 126896359555326745, 3153096762426186553, 82705881733348530241, 2293511922269658189121

Offset: 0

Author

Seiichi Manyama, Apr 20 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

Column k=3 of A362378.

Cf. A362380, A362479.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/2*exp(x)))))

Formula

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

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