A193282 a(n) = (n!/floor(n/2)!)^2.

1, 1, 4, 36, 144, 3600, 14400, 705600, 2822400, 228614400, 914457600, 110649369600, 442597478400, 74798973849600, 299195895398400, 67319076464640000, 269276305858560000, 77820852393123840000, 311283409572495360000, 112373310855670824960000

Offset: 0

Author

Peter Luschny, Sep 08 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A000142, A056040, A195009.

Programs

Magma

[(Factorial(n)/Factorial(Floor(n/2)))^2: n in [0..20]]; // Vincenzo Librandi, Sep 11 2011

Maple

A193282 := n -> (n!/iquo(n,2)!)^2;

Mathematica

Table[(n!/(Floor[n/2]!))^2,{n,0,20}] (* Harvey P. Dale, Jul 30 2020 *)

Formula

a(n) = A056040(n)*A000142(n).

a(n) = A081125(n)^2.

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A195009(n,k).

a(n) = n!^2*[x^n] (1+x)*BesselI(0,2*x). Here [x^n]f(x) denotes the coefficient of x^n in f(x).

Conjecture: a(n) + 8*a(n-1) - 4*(n-2)*(n+2)*a(n-2) + 16*(-2*n^2 + 6*n - 3)*a(n-3) - 64*(n-3)^2*a(n-4) = 0. - R. J. Mathar, Oct 03 2014