A179442 a(n) = ((n-1)! * (n+1)!) / n.

2, 3, 16, 180, 3456, 100800, 4147200, 228614400, 16257024000, 1448500838400, 158018273280000, 20713561989120000, 3212195459235840000, 581636820654489600000, 121600871304831959040000

Offset: 1

Author

Jaroslav Krizek, Jul 14 2010

Keywords

• nonn

Examples

			a(5) = ((5-1)! * (5+1)!) / 5 = (4! * 6!) / 5 = (24 * 720) / 5 = 17280 / 5 = 3456.
a(5) = ((5 -1)!^2) * (5+1) = 24^2 * 6 = 3456.
		

Crossrefs

Cf. A001044, A020725, A175430, A229020, A261879.

Programs

Mathematica

Table[(n - 1)!*(n + 1)!/n, {n, 1, 15}] (* Amiram Eldar, Jan 18 2021 *)

PARI

a(n) = (n-1)!^2*(n+1) \\ Charles R Greathouse IV, Oct 23 2023

Formula

a(n) = Product_{k=1..n} (k * A020725(k)) / (n^2) = Product_{k=1..n} (k * (k+1)) / (n^2).

a(n) = A175430(n) / n = A001044(n-1) * (n+1) = ((n -1)^2)! * (n+1).

G.f.: 1 + G(0), where G(k)= 1 + x*(k+1)/(1 - (k+2)/(k+2 + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 08 2013

From Amiram Eldar, Jan 18 2021: (Start)

Sum_{n>=1} 1/a(n) = BesselI(2,2) + BesselI(3,2) = A229020 + A261879.

Sum_{n>=1} (-1)^(n+1)/a(n) = BesselJ(2,2) - BesselJ(3,2). (End)