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.

1, 13, 184, 2701, 40456, 306860, 9391936, 144644749, 2238445480, 17386135604, 541801226176, 2115779182678, 132472258939840, 1038616414507808, 32621327116946944, 512963507737401997, 8075477240446327528, 63629398756188443588, 2007225253307641799872, 7921211894405933627674, 500517296244244008379456

Offset: 0

Author

Wolfdieter Lang, Jun 30 2016

Keywords

• nonn
• frac
• easy

Comments

For the denominators see A274346.

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.

Examples

			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, ...
		

Crossrefs

Cf. A227503, A274346.

Programs

Mathematica

(* See the program for r(n-1), n >= 1, in A274346. *)

Formula

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

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