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