A271925 Numerator of (Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).

3, 5, 87, 156, 913, 1693, 69769, 658529, 5002953, 173619, 1616141, 3107877, 239756907, 3244922897, 3402714857, 6606018008, 51386679347, 5504537914811, 622652618545649, 10572475711004, 10931562934889, 235301799307039, 4608689892802861, 9034390134407023, 488936376609325, 959905250448181

Offset: 1

Author

N. J. A. Sloane, May 04 2016

Keywords

• nonn
• frac

Examples

			3, 5, 87/13, 156/19, 913/95, 1693/155, 69769/5735, 658529/49321, 5002953/345247, 173619/11137, 1616141/97051, 3107877/175741, 239756907/12829093, ...
		

Links

• Jan de Gier, Loops, matchings and alternating-sign matrices, arXiv:math/0211285 [math.CO], 2002-2003.

Crossrefs

Sequences of fractions from de Gier paper: A271919-A271926.

Cf. A271926 (denominators), A073005, A186706.

Programs

Maple

f3:=proc(n) local j;
(mul(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1); end;
t3:=[seq(f3(n),n=1..50)];
map(numer,t3);
map(denom,t3);

Mathematica

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 *)

Formula

a(n)/A271926(n) ~ c * (2*n)^(2/3), where c = Gamma(1/3)*3^(3/2)/(2*Pi) = 3*A073005/A186706. - Amiram Eldar, Aug 17 2025