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 A274345 Numerators of coefficients in the expansion of (log(q) - log(k^2/16))/(8*k^2/16) in powers of k^2/16, where q is the Jacobi nome and k^2 the parameter of elliptic functions. 3

%I #12 Jul 01 2016 13:27:04

%S 1,13,184,2701,40456,306860,9391936,144644749,2238445480,17386135604,

%T 541801226176,2115779182678,132472258939840,1038616414507808,

%U 32621327116946944,512963507737401997,8075477240446327528,63629398756188443588,2007225253307641799872,7921211894405933627674,500517296244244008379456

%N Numerators of coefficients in the expansion of (log(q) - log(k^2/16))/(8*k^2/16) in powers of k^2/16, where q is the Jacobi nome and k^2 the parameter of elliptic functions.

%C For the denominators see A274346.

%C The rationals r(n) = a(n)/A274346(n) are given by A227503(n+1)/(n+1) reduced to lowest terms. See A227503 for details, references and links.

%F a(n) = numerator(A227503(n+1)/(n+1)), n >= 0.

%F (log(q) - log(k^2/16))/(8*k^2/16) = Sum_{n >= 0} (a(n)/A274346(n))*(k^2/16)^n.

%e The first rationals r(n) = a(n)/A274346(n) are: 1/1, 13/2, 184/3, 2701/4, 40456/5, 306860/3, 9391936/7, 144644749/8, 2238445480/9, 17386135604/5, 541801226176/11, 2115779182678/3, 132472258939840/13, 1038616414507808/7, 32621327116946944/15, ...

%t See the program for r(n-1), n >= 1, in

%t A274346.

%Y Cf. A227503, A274346.

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 30 2016

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