A361214 E.g.f. satisfies A(x) = exp( 3*x*A(x) / (1+x) ).

1, 3, 21, 288, 5841, 158148, 5370003, 219641922, 10518990129, 577629889848, 35788733371179, 2470154920005798, 187970878034549001, 15636177199793409444, 1411635193678825868979, 137469669176542404342042, 14364540773583252035937633

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..338

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

Formula

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

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

E.g.f.: -(1+x)/(3*x) * LambertW(-3*x/(1+x)).

Prog

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

Crossrefs

Cf. A335945, A361213.

Cf. A361069, A361194.

Sequence in context: A370741 A000681 A222035 * A171201 A193206 A055555

Adjacent sequences: A361211 A361212 A361213 * A361215 A361216 A361217

Keyword

nonn

Author

Seiichi Manyama, Mar 04 2023

Status

approved