A271920 - OEIS

%I #16 Mar 26 2018 06:06:38

%S 1,5,10,11,22,187,935,1955,391,11339,45356,1334,2668,27347,601634,

%T 614713,6147130,162898945,11847196,12051458,24102916,30128645,

%U 512186965,7273054903,7273054903,80003603933,400018019665,809792576395,9526971487,77081860213,1772882784899,188604551585,188604551585

%N Denominator of 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.CO/0211285, 2002-2003.

%e 1, 4/5, 7/10, 7/11, 13/22, 104/187, 494/935, 988/1955, 190/391, 5320/11339, 20615/45356, 589/1334, 1147/2668, 11470/27347, ...

%p f:=proc(n) local j;

%p mul(((3*j+1)/(3*j+2)),j=1..n-1); end;

%p t1:=[seq(f(n),n=1..50)];

%p map(numer,t1);

%p map(denom,t1);

%t Table[Product[(3*j+1)/(3*j+2), {j, 1, n-1}] // Denominator, {n, 1, 33}] (* _Jean-François Alcover_, Mar 25 2018 *)

%o (PARI) a(n) = denominator(prod(j=1, n-1, (3*j+1)/(3*j+2))); \\ _Michel Marcus_, Mar 25 2018

%Y Cf. A271919 (numerators).

%Y Other sequences of fractions from de Gier paper: A271921, A271922, A271923, A271924, A271925, A271926.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_, May 04 2016