A363354 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^3)).

1, 1, 3, 25, 277, 4221, 81421, 1891429, 51638217, 1618907257, 57332786041, 2264047223241, 98641443498973, 4700569138096885, 243213757144477029, 13579261873673960941, 813757288951509415441, 52098716516012891238129, 3548972379593741013388657

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( x - LambertW(-3*x^2*exp(3*x))/3 ).

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

Prog

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

Crossrefs

Cf. A125500, A143768, A363529.

Cf. A212917.

Sequence in context: A126746 A118989 A229162 * A347255 A292111 A123989

Adjacent sequences: A363351 A363352 A363353 * A363355 A363356 A363357

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved