A271924 Denominator of (1/3)*(Product_{j=0..n-1} (((2*j+1)*(3*j+4))/((j+1)*(6*j+1))) - 1).

1, 3, 13, 19, 285, 465, 17205, 147963, 345247, 11137, 291153, 175741, 12829093, 494964309, 494964309, 919219431, 6858791139, 706455487317, 77003648117553, 1262354887173, 1262354887173, 26321041453443, 500099787615417, 952244801075931, 50118147425049, 95795446344081

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) // Denominator;
Array[a, 26] (* Jean-François Alcover, Nov 30 2017 *)

Crossrefs

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

Sequence in context: A294676 A293465 A353251 * A354427 A178712 A273686

Adjacent sequences: A271921 A271922 A271923 * A271925 A271926 A271927

Keyword

nonn,frac

Author

N. J. A. Sloane, May 04 2016

Status

approved