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 A318711 Denominator of the coefficient of z^(-2*n) in the Stirling-like asymptotic expansion of G(z+1), where G(z) is Barnes G-function. 2
 1, 720, 7257600, 15676416000, 3476402012160000, 3320318656512000000, 4919915372473221120000000, 4632289550697863577600000000, 507464726196802564122476544000000000, 173072180302909506079665684480000000000, 49554442037561776763544469977956352000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS G(z+1) ~ A^(-1)*z^(-z^2/2-z/2-1/12)*exp(z^2/4)*(Gamma(z+1))^z*(Sum_{n>=0} b(n)/z^(2*n)), where A is the Glaisher-Kinkelin constant and Gamma is the gamma function. a(n) is the denominator of b(n). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..149 Chao-Ping Chen, Asymptotic expansions for Barnes G-function, Journal of Number Theory 135 (2014) 36-42. Eric Weisstein's World of Mathematics, Barnes G-Function FORMULA Let B_n be the Bernoulli number, and define the sequence {c_n} by the recurrence c_0 = 1, c_n = (1/(2*n)) * Sum_{k=0..n-1} B_{2*n-2*k+2}*c_k/((2*n-2*k+1)*(2*n-2*k+2)) for n > 0. a(n) is the denominator of c_n. EXAMPLE G(z+1) ~ A^(-1)*z^(-z^2/2-z/2-1/12)*exp(z^2/4)*(Gamma(z+1))^z*(1 - 1/(720*z^2) + 1447/(7257600*z^4) - 1559527/(15676416000*z^6) + 366331136219/(3476402012160000*z^8) - 637231027521743/(3320318656512000000*z^10) + ... ). CROSSREFS Cf. A143476, A318710. Sequence in context: A010799 A283830 A075754 * A143476 A008979 A158044 Adjacent sequences:  A318708 A318709 A318710 * A318712 A318713 A318714 KEYWORD nonn,frac AUTHOR Seiichi Manyama, Sep 01 2018 STATUS approved

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Last modified September 30 20:19 EDT 2020. Contains 337440 sequences. (Running on oeis4.)