A271919 Numerator of Product_{j=1..n-1} ((3*j+1)/(3*j+2)).

1, 4, 7, 7, 13, 104, 494, 988, 190, 5320, 20615, 589, 1147, 11470, 246605, 246605, 2416729, 62834954, 4488211, 4488211, 8831641, 10869712, 182067676, 2548947464, 2514502228, 27300309904, 134795280151, 269590560302, 3134773957, 25078191656, 570528860174, 60055669492, 59442856538

Offset: 1

Author

N. J. A. Sloane, May 04 2016

Keywords

• nonn
• frac

Examples

			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, ...
		

Links

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

Crossrefs

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

Cf. A271920 (denominators), A002161, A203145.

Programs

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

a[n_] := Product[(3j + 1)/(3j + 2), {j, 1, n - 1}] // Numerator;
Array[a, 33] (* Jean-François Alcover, Nov 17 2017 *)

PARI

a(n) = numerator(prod(j=1, n-1, ((3*j+1)/(3*j+2)))); \\ Michel Marcus, Nov 17 2017

Formula

a(n)/A271920(n) ~ c * (4/n)^(1/3), where c = Gamma(5/6)/sqrt(Pi) = A203145/A002161. - Amiram Eldar, Aug 17 2025