|
%I #11 Oct 13 2017 04:19:15
%S 1,1,13,19,95,155,5735,49321,345247,11137,97051,175741,12829093,
%T 164988103,164988103,306406477,2286263713,235485162439,25667882705851,
%U 420784962391,420784962391,8773680484481,166699929205139,317414933691977,16706049141683,31931815448027,5013295025340239
%N Denominator of (Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).
%H J. de Gier, <a href="http://arXiv.org/abs/math.CO/0211285">Loops, matchings and alternating-sign matrices</a>, arXiv:math.CO/0211285, 2002.
%e 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 f3:=proc(n) local j;
%p (mul(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1); end;
%p t3:=[seq(f3(n),n=1..50)];
%p map(numer,t3);
%p map(denom,t3);
%t Table[Product[(2*j+1)*(3*j+4)/((j+1)*(6*j+1)),{j,0,n-1}]-1, {n,1,20}]//Denominator (* _Vaclav Kotesovec_, Oct 13 2017 *)
%Y Sequences of fractions from de Gier paper: A271919-A271926.
%K nonn,frac
%O 1,3
%A _N. J. A. Sloane_, May 04 2016
|
