A271922 - OEIS

A271922

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

1, 5, 10, 11, 22, 187, 935, 1955, 391, 11339, 45356, 667, 2668, 27347, 601634, 614713, 6147130, 162898945, 11847196, 6025729, 24102916, 30128645, 512186965, 7273054903, 7273054903, 80003603933, 400018019665, 809792576395, 9526971487, 77081860213, 1772882784899, 188604551585, 188604551585

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OFFSET

1,2

LINKS

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

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

EXAMPLE

1, 8/5, 21/10, 28/11, 65/22, 624/187, 3458/935, 7904/1955, 1710/391, 53200/ 11339, 226765/45356, 3534/667, 14911/2668, 160580/27347, 3699075/601634, ...

MAPLE

f:=proc(n) local j;

mul(((3*j+1)/(3*j+2)), j=1..n-1); end;

t2:=[seq(n*f(n), n=1..50)];

map(numer, t2);

map(denom, t2);

MATHEMATICA

Table[Denominator[n Product[(3j+1)/(3j+2), {j, 1, n-1}]], {n, 1, 33}] (* Jean-François Alcover, Dec 16 2018 *)

PROG

(PARI) a(n) = denominator(n*prod(j=1, n-1, (3*j + 1)/(3*j + 2))); \\ Michel Marcus, Dec 16 2018

CROSSREFS

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