A362661 E.g.f. satisfies A(x) = exp( x * exp(x^3/6) * A(x) ).

1, 1, 3, 16, 129, 1356, 17767, 279714, 5149209, 108591688, 2582351451, 68380940904, 1995777685717, 63659665732716, 2203395556479951, 82253291389678756, 3294326092613575473, 140911264444599281616, 6411278790217738946899

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A273954, A362660.

Cf. A143567, A354551, A362655.

Sequence in context: A208829 A289145 A340341 * A368791 A135752 A218827

Adjacent sequences: A362658 A362659 A362660 * A362662 A362663 A362664

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2023

Status

approved