A362475 E.g.f. satisfies A(x) = exp(x + 3*x^2/2 * A(x)^2).

1, 1, 4, 28, 298, 4186, 74116, 1578340, 39394972, 1127378332, 36411516496, 1310173698736, 51982859674648, 2254757407407064, 106150698182657584, 5390926011965379376, 293782337188718257936, 17100576708082841577232, 1058920120014192744673600

Offset: 0

Author

Seiichi Manyama, Apr 21 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..370
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=3 of A362483.

Cf. A143768, A362474.

Cf. A362380.

Programs

PARI

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

Formula

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

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