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 A271923 #18 Aug 17 2025 01:51:07
%S A271923 1,5,29,52,913,1693,69769,658529,1667651,57873,1616141,1035959,
%T A271923 79918969,3244922897,3402714857,6606018008,51386679347,5504537914811,
%U A271923 622652618545649,10572475711004,10931562934889,235301799307039,4608689892802861,9034390134407023,488936376609325,959905250448181
%N A271923 Numerator of (1/3)*(Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).
%H A271923 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 A271923 a(n)/A271924(n) ~ c * (2*n)^(2/3), where c = Gamma(1/3)*sqrt(3)/(2*Pi) = A073005/A186706. - _Amiram Eldar_, Aug 17 2025
%e A271923 1, 5/3, 29/13, 52/19, 913/285, 1693/465, 69769/17205, 658529/147963, 1667651/ 345247, 57873/11137, 1616141/291153, 1035959/175741, 79918969/12829093, ...
%p A271923 f3:=proc(n) local j;
%p A271923 (1/3)*(mul(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1); end;
%p A271923 t3:=[seq(f3(n),n=1..50)];
%p A271923 map(numer,t3);
%p A271923 map(denom,t3);
%t A271923 a[n_] := (1/3)*(Product[((2*j + 1)*(3*j + 4))/((j + 1)*(6*j + 1)), {j, 0, n - 1}] - 1) // Numerator;
%t A271923 Array[a, 26] (* _Jean-François Alcover_, Nov 30 2017 *)
%Y A271923 Sequences of fractions from de Gier paper: A271919-A271926.
%Y A271923 Cf. A271924 (denominators), A073005, A186706.
%K A271923 nonn,frac
%O A271923 1,2
%A A271923 _N. J. A. Sloane_, May 04 2016