A362748 E.g.f. satisfies A(x) = exp(x^3/6 + x * A(x)).

1, 1, 3, 17, 133, 1386, 18097, 284299, 5225985, 110097836, 2616190831, 69236871309, 2019833025157, 64403044165942, 2228441614038837, 83166830262851591, 3330183199746011713, 142418071427679810936, 6478769455582913796475

Offset: 0

Author

Seiichi Manyama, May 02 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A349562, A362747.

Cf. A362381, A362691.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^3/6-lambertw(-x*exp(x^3/6)))))

Formula

E.g.f.: -LambertW(-x * exp(x^3/6)) / x = exp( x^3/6 - LambertW(-x*exp(x^3/6)) ).

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