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A296627 a(n) = BarnesG(4*n). 0
0, 2, 24883200, 6658606584104736522240000000, 69113789582492712943486800506462734562847413501952000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Barnes G-Function.
Wikipedia, Barnes G-function.
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.
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}]]
CROSSREFS
Sequence in context: A157992 A322145 A301810 * A247214 A367833 A135235
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 17 2017
STATUS
approved

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Last modified July 12 12:19 EDT 2024. Contains 374247 sequences. (Running on oeis4.)