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 A271925 #15 Aug 17 2025 02:49:55
%S A271925 3,5,87,156,913,1693,69769,658529,5002953,173619,1616141,3107877,
%T A271925 239756907,3244922897,3402714857,6606018008,51386679347,5504537914811,
%U A271925 622652618545649,10572475711004,10931562934889,235301799307039,4608689892802861,9034390134407023,488936376609325,959905250448181
%N A271925 Numerator of (Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).
%H A271925 Jan de Gier, <a href="http://arXiv.org/abs/math.CO/0211285">Loops, matchings and alternating-sign matrices</a>, arXiv:math/0211285 [math.CO], 2002-2003.
%F A271925 a(n)/A271926(n) ~ c * (2*n)^(2/3), where c = Gamma(1/3)*3^(3/2)/(2*Pi) = 3*A073005/A186706. - _Amiram Eldar_, Aug 17 2025
%e A271925 3, 5, 87/13, 156/19, 913/95, 1693/155, 69769/5735, 658529/49321, 5002953/345247, 173619/11137, 1616141/97051, 3107877/175741, 239756907/12829093, ...
%p A271925 f3:=proc(n) local j;
%p A271925 (mul(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1); end;
%p A271925 t3:=[seq(f3(n),n=1..50)];
%p A271925 map(numer,t3);
%p A271925 map(denom,t3);
%t A271925 Table[Product[(2*j+1)*(3*j+4)/((j+1)*(6*j+1)),{j,0,n-1}]-1, {n,1,20}]//Numerator (* _Vaclav Kotesovec_, Oct 13 2017 *)
%Y A271925 Sequences of fractions from de Gier paper: A271919-A271926.
%Y A271925 Cf. A271926 (denominators), A073005, A186706.
%K A271925 nonn,frac
%O A271925 1,1
%A A271925 _N. J. A. Sloane_, May 04 2016