A362477 E.g.f. satisfies A(x) = exp(x + x^3/6 * A(x)^3).

1, 1, 1, 2, 17, 161, 1351, 12391, 153385, 2388905, 40060781, 708351821, 13861042801, 305141790097, 7339275555067, 188198812659131, 5143808931521681, 150713978752271441, 4718460264313196665, 156524510548008965305, 5474266337362911068161

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..408
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=1 of A362490.

Cf. A362381.

Programs

PARI

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

Formula

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

a(n) = n! * Sum_{k=0..floor(n/3)} (1/6)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).