A175430 a(n) = (n-1)! * (n+1)!.

2, 6, 48, 720, 17280, 604800, 29030400, 1828915200, 146313216000, 14485008384000, 1738201006080000, 248562743869440000, 41758540970065920000, 8142915489162854400000, 1824013069572479385600000, 465123332740982243328000000, 133955519829402886078464000000

Offset

1,1

Comments

Also the number of automorphisms in the (n+1)-alternating group graph for n > 1. - Eric W. Weisstein, Jul 30 2018

Links

Amiram Eldar, Table of n, a(n) for n = 1..253

Eric Weisstein's World of Mathematics, Alternating Group Graph.

Eric Weisstein's World of Mathematics, Graph Automorphism.

Formula

a(n) = (Product_{k=1..n} k*A020725(k)) / n;

a(n) = (Product_{k=1..n} k*(k+1)) / n.

a(n) = (-1) * A129464(n) = A179442(n) * n. [Jaroslav Krizek, Jul 22 2010]

a(n) = 2*A010791(n-1). - Michel Marcus, Feb 03 2016

Sum_{n>=1} 1/a(n) = A229020 = BesselI(2,2). - Amiram Eldar, Oct 07 2020

Example

a(5) = (5-1)! * (5+1)! = 4! * 6! = 24 * 720 = 17280.
a(5) = ((1*2) * (2*3) * (3*4) * (4*5) * (5*6)) / 5 = 17280.

Mathematica

#[[1]] #[[3]] & /@ Partition[Range[0, 20]!, 3, 1] (* Harvey P. Dale, Jun 20 2017 *)
Table[(n - 1)! (n + 1)!, {n, 20}] (* or *) Table[Gamma[n] Gamma[n + 2], {n, 20}] (* Eric W. Weisstein, Jul 30 2018 *)

Prog

(PARI) a(n) = (n-1)! * (n+1)!; \\ Michel Marcus, Feb 03 2016

Crossrefs

Cf. A020725, A129464, A179442, A229020.

Sequence in context: A052717 A365287 A129464 * A003053 A113296 A275462

Adjacent sequences: A175427 A175428 A175429 * A175431 A175432 A175433

Keyword

nonn,easy

Author

Jaroslav Krizek, May 10 2010

Status

approved