A360939 E.g.f. satisfies A(x) = exp( 2*x*A(x) / (1-x) ).

1, 2, 16, 212, 4016, 99952, 3096448, 115063328, 4993598464, 248071645952, 13888585800704, 865481914527232, 59426130052458496, 4458258196636276736, 362864617248019800064, 31848507841521274769408, 2998685833332127139299328, 301504120063370711801724928

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..342

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

Formula

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

Prog

(PARI) a(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. A052868, A361212.

Cf. A361065.

Sequence in context: A349313 A364399 A365568 * A114531 A365585 A012056

Adjacent sequences: A360936 A360937 A360938 * A360940 A360941 A360942

Keyword

nonn

Author

Seiichi Manyama, Mar 04 2023

Status

approved