A151817 a(n) = 2*(2*n)!/n!.

2, 4, 24, 240, 3360, 60480, 1330560, 34594560, 1037836800, 35286451200, 1340885145600, 56317176115200, 2590590101299200, 129529505064960000, 6994593273507840000, 405686409863454720000, 25152557411534192640000, 1660068789161256714240000, 116204815241287969996800000

Offset: 0

Author

Roger L. Bagula, Jan 31 2009

Keywords

• nonn
• easy

Comments

(n+1)*a(n) is the number of random walk labelings of the comb graph of length n+1. - Sela Fried, Aug 02 2023

Links

• G. C. Greubel, Table of n, a(n) for n = 0..364
• Sela Fried and Toufik Mansour, Random walk labelings of perfect trees and other graphs, arXiv:2308.00315 [math.CO], 2023.

Crossrefs

Cf. A052718, A001813, row sums of A155951.

Programs

Mathematica

Table[2*(2*n)!/n!, {n, 0, 50}] (* G. C. Greubel, Feb 21 2017 *)

PARI

a(n)=2*(2*n)!/n! \\ Charles R Greathouse IV, Dec 05 2011

Formula

From Alexander R. Povolotsky, Jul 06 2009: (Start)

a(n) = 2^(2*n + 1)* Pochhammer(1/2, n).

a(n) = 2^(2*n + 1)*Gamma(n + 1/2) / Gamma(1/2) = 2^(2*n+1)*Gamma(n+1/2)/sqrt(Pi).

a(n) = 2*(2*n - 1)*a(n-1). (End) [Updated by Peter Luschny, Aug 02 2023]

E.g.f.: 2/(1-4*x)^(1/2).- Sergei N. Gladkovskii, Dec 05 2011

G.f.: G(0), where G(k)= 1 + 1/(1 - x*(4*k+2)/(x*(4*k+2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013

a(n) = A052718(n+1), n>0.

a(n) = 2*A001813(n). - R. J. Mathar, Mar 12 2017

Extensions

Typo in definition corrected by N. J. A. Sloane, Jul 12 2009

New name from Sergei N. Gladkovskii, Dec 05 2011