A271920 Denominator of Product_{j=1..n-1} ((3*j+1)/(3*j+2)).

1, 5, 10, 11, 22, 187, 935, 1955, 391, 11339, 45356, 1334, 2668, 27347, 601634, 614713, 6147130, 162898945, 11847196, 12051458, 24102916, 30128645, 512186965, 7273054903, 7273054903, 80003603933, 400018019665, 809792576395, 9526971487, 77081860213, 1772882784899, 188604551585, 188604551585

Offset

1,2

Links

Table of n, a(n) for n=1..33.

J. de Gier, Loops, matchings and alternating-sign matrices, arXiv:math.CO/0211285, 2002-2003.

Example

1, 4/5, 7/10, 7/11, 13/22, 104/187, 494/935, 988/1955, 190/391, 5320/11339, 20615/45356, 589/1334, 1147/2668, 11470/27347, ...

Maple

f:=proc(n) local j;
mul(((3*j+1)/(3*j+2)), j=1..n-1); end;
t1:=[seq(f(n), n=1..50)];
map(numer, t1);
map(denom, t1);

Mathematica

Table[Product[(3*j+1)/(3*j+2), {j, 1, n-1}] // Denominator, {n, 1, 33}] (* Jean-François Alcover, Mar 25 2018 *)

Prog

(PARI) a(n) = denominator(prod(j=1, n-1, (3*j+1)/(3*j+2))); \\ Michel Marcus, Mar 25 2018

Crossrefs

Cf. A271919 (numerators).

Other sequences of fractions from de Gier paper: A271921, A271922, A271923, A271924, A271925, A271926.

Sequence in context: A033894 A033649 A271922 * A329773 A213520 A241145

Adjacent sequences: A271917 A271918 A271919 * A271921 A271922 A271923

Keyword

nonn,frac

Author

N. J. A. Sloane, May 04 2016

Status

approved