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

%I A175430 #24 Feb 16 2025 08:33:12
%S A175430 2,6,48,720,17280,604800,29030400,1828915200,146313216000,
%T A175430 14485008384000,1738201006080000,248562743869440000,
%U A175430 41758540970065920000,8142915489162854400000,1824013069572479385600000,465123332740982243328000000,133955519829402886078464000000
%N A175430 a(n) = (n-1)! * (n+1)!.
%C A175430 Also the number of automorphisms in the (n+1)-alternating group graph for n > 1. - _Eric W. Weisstein_, Jul 30 2018
%H A175430 Amiram Eldar, <a href="/A175430/b175430.txt">Table of n, a(n) for n = 1..253</a>
%H A175430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlternatingGroupGraph.html">Alternating Group Graph</a>.
%H A175430 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>.
%F A175430 a(n) = (Product_{k=1..n} k*A020725(k)) / n;
%F A175430 a(n) = (Product_{k=1..n} k*(k+1)) / n.
%F A175430 a(n) = (-1) * A129464(n) = A179442(n) * n. [_Jaroslav Krizek_, Jul 22 2010]
%F A175430 a(n) = 2*A010791(n-1). - _Michel Marcus_, Feb 03 2016
%F A175430 Sum_{n>=1} 1/a(n) = A229020 = BesselI(2,2). - _Amiram Eldar_, Oct 07 2020
%e A175430 a(5) = (5-1)! * (5+1)! = 4! * 6! = 24 * 720 = 17280.
%e A175430 a(5) = ((1*2) * (2*3) * (3*4) * (4*5) * (5*6)) / 5 = 17280.
%t A175430 #[[1]] #[[3]] & /@ Partition[Range[0, 20]!, 3, 1] (* _Harvey P. Dale_, Jun 20 2017 *)
%t A175430 Table[(n - 1)! (n + 1)!, {n, 20}] (* or *) Table[Gamma[n] Gamma[n + 2], {n, 20}] (* _Eric W. Weisstein_, Jul 30 2018 *)
%o A175430 (PARI) a(n) = (n-1)! * (n+1)!; \\ _Michel Marcus_, Feb 03 2016
%Y A175430 Cf. A020725, A129464, A179442, A229020.
%K A175430 nonn,easy
%O A175430 1,1
%A A175430 _Jaroslav Krizek_, May 10 2010