A378017 E.g.f. satisfies A(x) = (1+x)^2 * exp( x * (1+x) * A(x) ).

1, 3, 15, 148, 2077, 38326, 883369, 24431436, 789531705, 29213730010, 1218401262541, 56566561281616, 2893886178904549, 161768999193007974, 9811122121462081281, 641683497800057913556, 45022670799746182036465, 3373421864644139722767538, 268843153008388446079159573

Offset

0,2

Links

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

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

Formula

E.g.f.: (1+x)^2 * exp( -LambertW(-x * (1+x)^3) ).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^2*exp(-lambertw(-x*(1+x)^3))))
(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+2, n-k)/k!);

Crossrefs

Cf. A376145, A377828, A378016.

Cf. A377966.

Sequence in context: A230367 A293844 A181535 * A162078 A245069 A317667

Adjacent sequences: A378014 A378015 A378016 * A378018 A378019 A378020

Keyword

nonn

Author

Seiichi Manyama, Nov 14 2024

Status

approved