A362691 E.g.f. satisfies A(x) = exp(x^3 + x * A(x)).

1, 1, 3, 22, 173, 1836, 24847, 403474, 7667865, 167097016, 4108985531, 112562882334, 3399748630357, 112246652293972, 4022094151907847, 155461592488721866, 6447531477912609713, 285606134199075271536, 13458367778796518816755

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.: -LambertW(-x * exp(x^3)) / x = exp( x^3 - LambertW(-x*exp(x^3)) ).

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

Prog

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

Crossrefs

Cf. A349562, A362690.

Cf. A362737.

Sequence in context: A290719 A074576 A077244 * A138899 A147855 A354327

Adjacent sequences: A362688 A362689 A362690 * A362692 A362693 A362694

Keyword

nonn

Author

Seiichi Manyama, May 01 2023

Status

approved