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 A241755 #23 Nov 11 2016 15:52:02
%S A241755 1,1,27,125,42875,250047,12326391,78953589,266468362875,1795828623875,
%T A241755 98540708249269,685638992559339,308969245276647319,
%U A241755 2197380271937921875,126096314555551359375,911218671317138401125,27146115437208870107914875
%N A241755 A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean's problem, numerators).
%C A241755 Quoted from SIAM: This sum arises from the calculation of the shift of the frequency of an electromagnetic transverse magnetic wave-mode caused by a small metallic cylinder in a resonant cavity.
%D A241755 E. S. Andersen and M. E. Larsen. A finite sum of products of binomial coefficients, Problem 92-18, by C. C. Grosjean, Solution. SIAM Rev. 35 (1993), 645-646.
%H A241755 P. Flajolet, B. Salvy, and Helmut Prodinger, <a href="http://dx.doi.org/10.1137/1035147">A Finite Sum of Products of Binomial Coefficients</a>, Problem 92-18 by C. C. Grosjean, Solution. SIAM Rev. 35 (1993), 645-646.
%H A241755 C. C. Grosjean, <a href="http://dx.doi.org/10.1137/1034122">Problem no. 92-18</a>, SIAM Rev. 34 (1992), p. 649.
%H A241755 M. E. Larsen, <a href="http://www.math.ku.dk/~mel/larsen.pdf">Summa Summarum</a>, page 114.
%F A241755 GAMMA(3/4)^2 * 4F3(1/4, 1/4, -n, -n; 1, 3/4-n, 3/4-n; 1)/(GAMMA(3/4-n)^2*GAMMA(n+1)^2).
%F A241755 binomial(2n, n)^2*binomial(n-1/2, 2n)*(-1/4)^n.
%e A241755 1, 1/8, 27/512, 125/4096, 42875/2097152, 250047/16777216, ...
%t A241755 a[n_] := Binomial[2*n, n]^2*Binomial[n-1/2, 2*n]*(-1/4)^n; Table[a[n]//Numerator, {n, 0, 20}]
%Y A241755 Cf. A241756.
%K A241755 nonn,frac
%O A241755 0,3
%A A241755 _Jean-François Alcover_, Apr 28 2014