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%I #11 Nov 30 2017 08:04:06
%S 1,3,13,19,285,465,17205,147963,345247,11137,291153,175741,12829093,
%T 494964309,494964309,919219431,6858791139,706455487317,77003648117553,
%U 1262354887173,1262354887173,26321041453443,500099787615417,952244801075931,50118147425049,95795446344081
%N Denominator of (1/3)*(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 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 f3:=proc(n) local j;
%p (1/3)*(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 a[n_] := (1/3)*(Product[((2*j + 1)*(3*j + 4))/((j + 1)*(6*j + 1)), {j, 0, n - 1}] - 1) // Denominator;
%t Array[a, 26] (* _Jean-François Alcover_, Nov 30 2017 *)
%Y Sequences of fractions from de Gier paper: A271919-A271926.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, May 04 2016
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