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 A111876 #22 Jul 24 2023 02:38:08
%S A111876 1,6,30,420,1260,13860,180180,72072,1225224,116396280,116396280,
%T A111876 2677114440,13385572200,5736673800,166363540200,10314539492400,
%U A111876 10314539492400,72201776446800,2671465728531600,2671465728531600
%N A111876 Denominator of Sum_{k = 0..n} 1/((k+1)*(2*k+1)).
%H A111876 G. C. Greubel, <a href="/A111876/b111876.txt">Table of n, a(n) for n = 0..1000</a>
%F A111876 a(n) = denominator of ( digamma(n+3/2) - digamma(n+2) + 2*log(2) ).
%F A111876 a(n) = denominator of 2*(n+1)*Integral_{x = 0..1} x^n* log(1+sqrt(x)) dx.
%F A111876 a(n-1) = denominator( (1/n)*Sum_{k = 1..n} (n - k)/(n + k) ). - _Peter Bala_, Oct 10 2021
%p A111876 seq(denom( add(1/((k+1)*(2*k+1)), k = 0..n) ), n = 0..20); # _Peter Bala_, Oct 10 2021
%t A111876 Table[Denominator[HarmonicNumber[2n+2] - HarmonicNumber[n+1]]/2, {n, 0, 30}]
%o A111876 (PARI) a(n) = denominator(sum(k=0, n, 1/((k+1)*(2*k+1)))); \\ _Michel Marcus_, Oct 10 2021
%o A111876 (Magma) [Denominator(HarmonicNumber(2*n+2) -HarmonicNumber(n+1))/2: n in [0..40]]; // _G. C. Greubel_, Jul 24 2023
%o A111876 (SageMath) [denominator(harmonic_number(2*n+2,1) - harmonic_number(n+1,1))/2 for n in range(41)] # _G. C. Greubel_, Jul 24 2023
%Y A111876 Cf. A082687 (numerators), A117664.
%K A111876 easy,nonn,frac
%O A111876 0,2
%A A111876 _Paul Barry_, Aug 19 2005