A362734 E.g.f. satisfies A(x) = exp(x + x * A(x)^3).

1, 2, 16, 296, 8512, 333632, 16595200, 1001460224, 71094759424, 5805799829504, 536188352856064, 55259197654089728, 6287146625230962688, 782751635353947865088, 105852868748672770244608, 15451195442132410179780608, 2421355190097788960505856000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..322

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

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

a(n) = Sum_{k=0..n} (3*k+1)^(n-1) * binomial(n,k) = 2^n * A349714(n).

a(n) ~ sqrt(LambertW(exp(-1)) + 1) * 3^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^(n + 1/3)). - Vaclav Kotesovec, Apr 24 2024

Prog

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

Crossrefs

Cf. A349562, A362693, A362694, A362735.

Cf. A349714, A362392, A362472.

Sequence in context: A188740 A259647 A188985 * A009250 A335618 A174487

Adjacent sequences: A362731 A362732 A362733 * A362735 A362736 A362737

Keyword

nonn

Author

Seiichi Manyama, May 01 2023

Status

approved