A296627 a(n) = BarnesG(4*n).

0, 2, 24883200, 6658606584104736522240000000, 69113789582492712943486800506462734562847413501952000000000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 17 2017

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Barnes G-Function.
• Wikipedia, Barnes G-function.

Crossrefs

Cf. A000178, A296607, A296608.

Programs

Mathematica

Table[BarnesG[4*n], {n, 0, 6}]
Round[Table[Glaisher^15 * E^(-5/4) * 2^(7/3 - 14*n + 16*n^2) * Pi^(3/2 - 6*n) * BarnesG[n] * BarnesG[1/4 + n]^2 * BarnesG[1/2 + n]^3 * BarnesG[3/4 + n]^4 * BarnesG[1 + n]^3 * BarnesG[5/4 + n]^2 * BarnesG[3/2 + n], {n, 0, 6}]]

Formula

a(n) = A^15 * exp(-5/4) * 2^(7/3 - 14*n + 16*n^2) * Pi^(3/2 - 6*n) * BarnesG(n) * BarnesG(1/4 + n)^2 * BarnesG(1/2 + n)^3 * BarnesG(3/4 + n)^4 * BarnesG(1 + n)^3 * BarnesG(5/4 + n)^2 * BarnesG(3/2 + n), where A is the Glaisher-Kinkelin constant A074962.

a(n) ~ 2^(16*n^2 - 6*n + 1/3) * n^(8*n^2 - 4*n + 5/12) * Pi^(2*n - 1/2) / (A * exp(12*n^2 - 4*n - 1/12)), where A is the Glaisher-Kinkelin constant A074962.