A165970 a(n) = sqrt( superfactorial(4n) / factorial(2n) ).

1, 12, 14515200, 420505587390873600000, 6848282921689337839624757371207680000000000, 592617982969061328644755583860005865281724398591341934673920000000000000000

Offset: 0

Author

Max Alekseyev, Oct 02 2009

Keywords

• nonn

Comments

For n>=5, 2^(12*n)*10^(12*(n - 4)) | a(n). - G. C. Greubel, Apr 18 2016

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..14

Crossrefs

Cf. A168467.

Programs

Mathematica

Table[Sqrt[Product[k!,{k,0,4*n}]/(2*n)!],{n,0,10}] (* Vaclav Kotesovec, Jul 10 2015 *)

PARI

{a(n) = 2^n*prod(k=1, 2*n, (2*k-1)!)} \\ Seiichi Manyama, Jul 05 2019

Formula

a(n) = sqrt( A000178(4n) / A000142(2n) ) = sqrt(0! * 1! * ... * (2n-1)! * (2n+1)! * (2n+2)! * ... * (4n)!).

a(n) ~ 2^(8*n^2 + 4*n + 1/6) * n^(4*n^2 + n - 1/24) * Pi^n / (A^(1/2) * exp(6*n^2 + n - 1/24)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015

a(n) = 2^n * Product_{k=1..2*n} (2*k-1)!. - Seiichi Manyama, Jul 05 2019

a(n) = A^(3/2) * exp(-1/8) * 2^(4*n^2 + n - 1/24) * BarnesG(2*n + 3/2) * BarnesG(2*n + 1) / Pi^(n + 1/4), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jul 05 2019