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 A372140 a(n) = Product_{k=1..n} BarnesG(k)^k. 1
 1, 1, 1, 1, 16, 3981312, 2271857773302207479808, 133781874275586180035265927852035878702421114880000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The next term has 113 digits. LINKS Table of n, a(n) for n=0..7. Eric Weisstein's World of Mathematics, Barnes G-Function. Wikipedia, Barnes G-function. FORMULA a(n) ~ (2*Pi)^(n*(n^2 - 1)/6) * n^(n^4/8 - n^3/12 - n^2/6 + n/24 + 19/720) / (A^(n^2/2 + n/2 - 1/3) * exp(7*n^4/32 - 5*n^3/72 - 7*n^2/24 - n/24 - zeta(3)/(8*Pi^2) + zeta'(-3)/6 + 23/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068. MATHEMATICA Table[Product[BarnesG[k]^k, {k, 1, n}], {n, 0, 8}] CROSSREFS Cf. A055462, A255269. Sequence in context: A013804 A116102 A323336 * A356084 A369821 A013878 Adjacent sequences: A372137 A372138 A372139 * A372141 A372142 A372143 KEYWORD nonn AUTHOR Vaclav Kotesovec, Apr 20 2024 STATUS approved

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Last modified August 9 15:46 EDT 2024. Contains 375044 sequences. (Running on oeis4.)