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 A271921 #20 Aug 17 2025 02:07:50
%S A271921 1,8,21,28,65,624,3458,7904,1710,53200,226765,3534,14911,160580,
%T A271921 3699075,3945680,41084393,1131029172,85276009,44882110,185464461,
%U A271921 239133664,4187556548,61174739136,62862555700,709808057504,3639472564077,7548535688456,90908444753,752345749680,17686394665394
%N A271921 Numerator of n*Product_{j=1..n-1} ((3*j + 1)/(3*j + 2)).
%H A271921 Jan de Gier, <a href="https://arxiv.org/abs/math/0211285">Loops, matchings and alternating-sign matrices</a>, arXiv:math/0211285 [math.CO], 2002-2003.
%F A271921 a(n)/A271922(n) ~ c * (2*n)^(2/3), where c = Gamma(5/6)/sqrt(Pi) = A203145/A002161. - _Amiram Eldar_, Aug 17 2025
%e A271921 1, 8/5, 21/10, 28/11, 65/22, 624/187, 3458/935, 7904/1955, 1710/391, 53200/ 11339, 226765/45356, 3534/667, 14911/2668, 160580/27347, 3699075/601634, ...
%p A271921 f:=proc(n) local j;
%p A271921 mul(((3*j+1)/(3*j+2)),j=1..n-1); end;
%p A271921 t2:=[seq(n*f(n),n=1..50)];
%p A271921 map(numer,t2);
%p A271921 map(denom,t2);
%t A271921 Table[n*Product[(3*j+1)/(3*j+2), {j, 1, n-1}] // Numerator, {n, 1, 31}] (* _Jean-François Alcover_, Mar 25 2018 *)
%o A271921 (PARI) a(n) = numerator(n*prod(j=1, n-1, (3*j + 1)/(3*j + 2))); \\ _Michel Marcus_, Mar 25 2018
%Y A271921 Cf. A271922 (denominators), A002161, A203145.
%Y A271921 Sequences of fractions from de Gier paper: A271919, A271920, A271922, A271923, A271924, A271925, A271926.
%K A271921 nonn,frac
%O A271921 1,2
%A A271921 _N. J. A. Sloane_, May 04 2016