A264389 Denominator of binomial(n-1, 2)/(6*n), for n >= 1. Denominator of Dedekind sum s(1,n).

1, 1, 18, 8, 5, 18, 14, 16, 27, 5, 22, 72, 13, 14, 90, 32, 17, 27, 38, 40, 63, 22, 46, 144, 25, 13, 162, 56, 29, 90, 62, 64, 99, 17, 70, 216, 37, 38, 234, 80, 41, 63, 86, 88, 135, 46, 94, 288, 49, 25, 306, 104, 53, 162, 110, 112, 171, 29, 118, 360, 61, 62, 378

Offset

1,3

Comments

See A264388 for the numerators and details about the Dedekind sum s(1,n), as well as references.

Links

Table of n, a(n) for n=1..63.

Formula

a(n) = denominator(binomial(n-1, 2)/(6*n)), n >= 1.

a(n) = denominator(s(1,n)), with s(1,n) = Sum_{r=1..(n-1)} (r/n)*(r/n - floor(r/n)- 1/2), n >= 1, where s(h,k) are the Dedekind sums.

Mathematica

Denominator[Table[Binomial[n-1, 2]/(6n), {n, 50}]] (* Harvey P. Dale, Aug 30 2016 *)

Prog

(Julia)
using Nemo
A264389(n) = denominator(dedekind_sum(1, n))
[A264389(n) for n in 1:70] |> println # Peter Luschny, Mar 13 2018

Crossrefs

Cf. A264388.

Sequence in context: A097534 A040310 A068610 * A104218 A033338 A337731

Adjacent sequences: A264386 A264387 A264388 * A264390 A264391 A264392

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jan 11 2016

Status

approved