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

0,1

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.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A052718, A001813, row sums of A155951.

Sequence in context: A141307 A190655 A038049 * A265937 A038058 A062531

Adjacent sequences: A151814 A151815 A151816 * A151818 A151819 A151820

Keyword

nonn,easy

Author

Roger L. Bagula, Jan 31 2009

Extensions

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

New name from Sergei N. Gladkovskii, Dec 05 2011

Status

approved