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%I #11 Oct 13 2017 04:20:21
%S 3,5,87,156,913,1693,69769,658529,5002953,173619,1616141,3107877,
%T 239756907,3244922897,3402714857,6606018008,51386679347,5504537914811,
%U 622652618545649,10572475711004,10931562934889,235301799307039,4608689892802861,9034390134407023,488936376609325,959905250448181
%N Numerator 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}]//Numerator (* _Vaclav Kotesovec_, Oct 13 2017 *)
%Y Sequences of fractions from de Gier paper: A271919-A271926.
%K nonn,frac
%O 1,1
%A _N. J. A. Sloane_, May 04 2016
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