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) = 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
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, May 10 2010
STATUS
approved