A271923 -id:A271923

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A271920

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, May 04 2016

STATUS

approved

A271921

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

+10
1

1, 8, 21, 28, 65, 624, 3458, 7904, 1710, 53200, 226765, 3534, 14911, 160580, 3699075, 3945680, 41084393, 1131029172, 85276009, 44882110, 185464461, 239133664, 4187556548, 61174739136, 62862555700, 709808057504, 3639472564077, 7548535688456, 90908444753, 752345749680, 17686394665394

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..31.

J. de Gier, Loops, matchings and alternating-sign matrices, arXiv:math.CO/0211285, 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[n*Product[(3*j+1)/(3*j+2), {j, 1, n-1}] // Numerator, {n, 1, 31}] (* Jean-François Alcover, Mar 25 2018 *)

PROG

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