OFFSET
0,2
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
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
MATHEMATICA
Table[Sqrt[Product[k!, {k, 0, 4*n}]/(2*n)!], {n, 0, 10}] (* Vaclav Kotesovec, Jul 10 2015 *)
PROG
(PARI) {a(n) = 2^n*prod(k=1, 2*n, (2*k-1)!)} \\ Seiichi Manyama, Jul 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Oct 02 2009
STATUS
approved