A271926 Denominator of (Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).

1, 1, 13, 19, 95, 155, 5735, 49321, 345247, 11137, 97051, 175741, 12829093, 164988103, 164988103, 306406477, 2286263713, 235485162439, 25667882705851, 420784962391, 420784962391, 8773680484481, 166699929205139, 317414933691977, 16706049141683, 31931815448027, 5013295025340239

Offset

1,3

Links

Table of n, a(n) for n=1..27.

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

Example

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

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}]//Denominator (* Vaclav Kotesovec, Oct 13 2017 *)

Crossrefs

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

Sequence in context: A158332 A241486 A180531 * A090258 A241246 A153266

Adjacent sequences: A271923 A271924 A271925 * A271927 A271928 A271929

Keyword

nonn,frac

Author

N. J. A. Sloane, May 04 2016

Status

approved