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%I #15 Dec 16 2018 03:30:06
%S 1,5,10,11,22,187,935,1955,391,11339,45356,667,2668,27347,601634,
%T 614713,6147130,162898945,11847196,6025729,24102916,30128645,
%U 512186965,7273054903,7273054903,80003603933,400018019665,809792576395,9526971487,77081860213,1772882784899,188604551585,188604551585
%N Denominator of n*Product_{j=1..n-1} ((3*j + 1)/(3*j + 2)).
%H J. de Gier, <a href="https://arxiv.org/abs/math/0211285">Loops, matchings and alternating-sign matrices</a>, arXiv:math/0211285 [math.CO], 2002-2003.
%e 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 f:=proc(n) local j;
%p mul(((3*j+1)/(3*j+2)),j=1..n-1); end;
%p t2:=[seq(n*f(n),n=1..50)];
%p map(numer,t2);
%p map(denom,t2);
%t Table[Denominator[n Product[(3j+1)/(3j+2), {j, 1, n-1}]], {n, 1, 33}] (* _Jean-François Alcover_, Dec 16 2018 *)
%o (PARI) a(n) = denominator(n*prod(j=1, n-1, (3*j + 1)/(3*j + 2))); \\ _Michel Marcus_, Dec 16 2018
%Y Sequences of fractions from de Gier paper: A271919-A271926.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, May 04 2016