cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, May 04 2016

Keywords

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

Crossrefs

Cf. A271919 (numerators).
Other sequences of fractions from de Gier paper: A271921, A271922, A271923, A271924, A271925, A271926.

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
    Table[Product[(3*j+1)/(3*j+2), {j, 1, n-1}] // Denominator, {n, 1, 33}] (* Jean-François Alcover, Mar 25 2018 *)
  • PARI
    a(n) = denominator(prod(j=1, n-1, (3*j+1)/(3*j+2))); \\ Michel Marcus, Mar 25 2018

A271921 Numerator of n*Product_{j=1..n-1} ((3*j + 1)/(3*j + 2)).

Original entry on oeis.org

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
Offset: 1

Views

Author

N. J. A. Sloane, May 04 2016

Keywords

Examples

			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, ...

Links

Crossrefs

Cf. A271922 (denominators), A002161, A203145.
Sequences of fractions from de Gier paper: A271919, A271920, A271922, A271923, A271924, A271925, A271926.

Programs

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

Formula

a(n)/A271922(n) ~ c * (2*n)^(2/3), where c = Gamma(5/6)/sqrt(Pi) = A203145/A002161. - Amiram Eldar, Aug 17 2025
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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