A362390 E.g.f. satisfies A(x) = exp(x + x^3/3 * A(x)).

1, 1, 1, 3, 17, 81, 441, 3641, 33825, 318753, 3505521, 45095601, 616484001, 9013086369, 145909533225, 2556431401161, 47388760825281, 937507626246081, 19840711661183457, 443937299529447009, 10456231167451597761, 259738234024404363201

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..434
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=2 of A362378.

Cf. A001470, A362478.

Programs

PARI

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

Formula

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

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