A271923 Numerator of (1/3)*(Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).

1, 5, 29, 52, 913, 1693, 69769, 658529, 1667651, 57873, 1616141, 1035959, 79918969, 3244922897, 3402714857, 6606018008, 51386679347, 5504537914811, 622652618545649, 10572475711004, 10931562934889, 235301799307039, 4608689892802861, 9034390134407023, 488936376609325, 959905250448181

Offset

1,2

Links

Table of n, a(n) for n=1..26.

J. de Gier, Loops, matchings and alternating-sign matrices, arXiv:math.CO/0211285, 2002.

Example

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, ...

Maple

f3:=proc(n) local j;
(1/3)*(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

a[n_] := (1/3)*(Product[((2*j + 1)*(3*j + 4))/((j + 1)*(6*j + 1)), {j, 0, n - 1}] - 1) // Numerator;
Array[a, 26] (* Jean-François Alcover, Nov 30 2017 *)

Crossrefs

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

Sequence in context: A146829 A329151 A201712 * A224499 A107003 A141374

Adjacent sequences: A271920 A271921 A271922 * A271924 A271925 A271926

Keyword

nonn,frac

Author

N. J. A. Sloane, May 04 2016

Status

approved