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.
%I A278714 #20 Sep 08 2022 08:46:18
%S A278714 1,18,1,14,27,22,13,18,17,38,63,46,5,162,29,62,99,14,37,234,41,86,27,
%T A278714 94,49,306,53,22,171,118,61,378,13,134,207,142,73,90,77,158,243,166,
%U A278714 17,522,89,182,279,38,97,594,101,206,63,214,109,666,113,46,351,238
%N A278714 Denominators of (n-1)*(n-3)/(6*(2*n-1)), for n >= 1. Denominators of Dedekind sum s(2, 2*n-1).
%C A278714 For the numerators see A278713, also for references and details.
%H A278714 Robert Israel, <a href="/A278714/b278714.txt">Table of n, a(n) for n = 1..10000</a>
%F A278714 a(n) = denominator((n-1)*(n-3)/(6*(2*n-1))) (in lowest terms), n >= 1.
%F A278714 a(n) = denominator(r(n)), with r(n) = s(2,2*n-1) where s(2,k) = Sum_{r=1..(k-1)} (r/k)*(2*r/k - floor(2*r/k)- 1/2), for odd k.
%F A278714 From _Robert Israel_, Dec 07 2016: (Start)
%F A278714 (2n+59) a(n) = (2n-1) a(n+30).
%F A278714 a(n) = 6(2n-1)/b(n) where
%F A278714 b(n) = 1 if n == 2, 14, 20, or 26 (mod 30)
%F A278714 b(n) = 2 if n == 5, 11, 17, or 29 (mod 30)
%F A278714 b(n) = 3 if n == 0, 4, 6, 10, 12, 16, 22, or 24 (mod 30)
%F A278714 b(n) = 5 if n == 8 (mod 30)
%F A278714 b(n) = 6 if n == 1, 7, 9, 15, 19, 21, 25, or 27 (mod 30)
%F A278714 b(n) = 10 if n == 23 (mod 30)
%F A278714 b(n) = 15 if n == 18 or 28 (mod 30)
%F A278714 b(n) = 30 if n == 3 or 13 (mod 30).
%F A278714 G.f.: x*(1+18*x+x^2+14*x^3+27*x^4+22*x^5+13*x^6+18*x^7+17*x^8+38*x^9+63*x^10+46*x^11
%F A278714 +5*x^12+162*x^13+29*x^14+62*x^15+99*x^16+14*x^17+37*x^18+234*x^19+41*x^20+86*x^21
%F A278714 +27*x^22+94*x^23+49*x^24+306*x^25+53*x^26+22*x^27+171*x^28+118*x^29+59*x^30
%F A278714 +342*x^31+11*x^32+106*x^33+153*x^34+98*x^35+47*x^36+54*x^37+43*x^38+82*x^39
%F A278714 +117*x^40+74*x^41+7*x^42+198*x^43+31*x^44+58*x^45+81*x^46+10*x^47+23*x^48
%F A278714 +126*x^49+19*x^50+34*x^51+9*x^52+26*x^53+11*x^54+54*x^55+7*x^56+2*x^57+9*x^58
%F A278714 +2*x^59)/(1-x^30)^2.
%F A278714 (End)
%p A278714 seq(denom((n-1)*(n-3)/(6*(2*n-1))),n=1..100); # _Robert Israel_, Dec 07 2016
%t A278714 Table[((n-1)(n-3))/(6(2n-1)),{n,60}]//Denominator (* _Harvey P. Dale_, Feb 10 2019 *)
%o A278714 (PARI) a(n) = denominator((n-1)*(n-3)/(6*(2*n-1))) \\ _Felix Fröhlich_, Nov 28 2016
%o A278714 (Magma) [Denominator((n-1)*(n-3)/(6*(2*n-1))): n in [1..60]]; // _Vincenzo Librandi_, Dec 08 2016
%Y A278714 Cf. A278713.
%K A278714 nonn,frac,easy
%O A278714 1,2
%A A278714 _Wolfdieter Lang_, Nov 28 2016