cp's OEIS Frontend

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

a(n) = A^(35/6) * exp(-35/72) * Gamma(1/3)^(5/3) * 2^(-125/72 + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * Pi^(-25/12 - 5*n/2) * BarnesG(1 + n) * BarnesG(7/6 + n) * BarnesG(4/3 + n) * BarnesG(3/2 + n) * BarnesG(5/3 + n) * BarnesG(11/6 + n), where A = A074962 is the Glaisher-Kinkelin constant.

a(n) ~ A^(-1/6) * Gamma(1/3)^(5/3) * 2^(-35/72 + 3*n + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * exp(1/72 - 5*n/2 - 9*n^2/2) * n^(19/72 + 5*n/2 + 3*n^2) * Pi^(-5/6 + n/2), where A = A074962 is the Glaisher-Kinkelin constant.