A361213 E.g.f. satisfies A(x) = exp( 2*x*A(x) / (1+x) ).

1, 2, 8, 68, 848, 14192, 298048, 7546016, 223792640, 7612381952, 292216807424, 12497875215872, 589392367925248, 30386736933804032, 1700376343771136000, 102641314849948602368, 6648428846464054919168, 459977466799800897437696

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..360

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

Formula

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

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

E.g.f.: -(1+x)/(2*x) * LambertW(-2*x/(1+x)).

a(n) ~ (2*exp(1) - 1)^(n + 1/2) * n^(n-1) / (sqrt(2) * exp(n - 1/2)). - Vaclav Kotesovec, Nov 10 2023

Prog

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

Crossrefs

Cf. A335945, A361214.

Cf. A361068, A361193.

Sequence in context: A053922 A030445 A093990 * A156448 A262479 A192550

Adjacent sequences: A361210 A361211 A361212 * A361214 A361215 A361216

Keyword

nonn

Author

Seiichi Manyama, Mar 04 2023

Status

approved