This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274655 #6 Jul 08 2016 17:47:46 %S A274655 0,1,21,185,18655,102501,1394239,33944053,3074289075,99205524275, %T A274655 7190934788323,4590859955591,2435122285235549,23468182735812325, %U A274655 38870446014205425,145536272272236993,280137373064011153371,1633533514217325226737,74200692627870055029475 %N A274655 Numerators of coefficients of z^n for the expansion of Fricke's hypergeometric function F_1(1/2,1/2;z). %C A274655 For the denominators see A274656. %C A274655 The main entry is A274653/A274654. In A274653 Fricke's hypergeometric function F_1(a,b;z) is defined by the recurrence. More details and the Fricke references are also found there. %F A274655 a(n) = numerator(R(n)), where the rationals (in lowest terms) are R(n) = [z^n]F_1(1/2,1/2;z), and the recurrence for R(n) = r(n)/n! is obtained from the one given for r(n) in A274653. %F A274655 R(n) = ((2*n-1)/(2*n))^2*R(n-1) + 2*C(n)/(n*(2*n-1)), n >= 1, R(0) = 0, with C(n) = ((2*n)!)^2 / (n!^4*2^(4*n)). %e A274655 The rationals R(n) begin: %e A274655 0, 1/2, 21/64, 185/768, 18655/98304, 102501/655360, 1394239/10485760, 33944053/293601280, ... %Y A274655 Cf. A274656, A274653/A274654. %K A274655 nonn,easy,frac %O A274655 0,3 %A A274655 _Wolfdieter Lang_, Jul 07 2016