A362479 E.g.f. satisfies A(x) = exp(x + x^3/2 * A(x)^3).

1, 1, 1, 4, 49, 481, 4471, 57751, 1036393, 19939753, 399150541, 9082285741, 237719388721, 6759766432849, 204408880370059, 6672899023062091, 236080878357745681, 8926817568378582481, 357421258163575234873, 15158257732928974255993

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..393
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=3 of A362490.

Cf. A362391.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3/2*exp(3*x))/3)))

Formula

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

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