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

1,1

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

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

Crossrefs

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

Sequence in context: A308612 A082715 A133660 * A236365 A057663 A056244

Adjacent sequences: A271922 A271923 A271924 * A271926 A271927 A271928

Keyword

nonn,frac

Author

N. J. A. Sloane, May 04 2016

Status

approved