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 A334000 #28 Apr 30 2020 14:56:12
%S A334000 0,1,11,122,1518,21423,340869,6058980,119218860,2575293165,
%T A334000 60628447215,1545696702270,42437227275450,1248581232985275,
%U A334000 39197268410049225,1307969571015966600,46233376386927067800,1725823391345415833625,67845041198360981737875
%N A334000 a(n) = (2*n+1)!! * Sum_{k=0..n} k/(2*k+1).
%F A334000 a(n) = (2*n+1)!!*(Sum_{k=0..n} k/(2*k+1)).
%F A334000 Recurrence: a(n) = 4*n*a(n-1)-(2*n-1)^2*a(n-2)+(2*n-1)!!.
%e A334000 a(3) = 122 since 0/1 + 1/3 + 2/5 + 3/7 = 122/105 = 122/(7!!).
%t A334000 Table[Sum[k/(2*k+1),{k,0,n}],{n,0,18}]*Table[Product[2*j+1,{j,0,n}],{n,0,18}]
%t A334000 FullSimplify[Table[((n+1)/2 - HarmonicNumber[n + 1/2]/4 - Log[2]/2) * (2*n+1)!!, {n, 0, 20}]] (* _Vaclav Kotesovec_, Apr 14 2020 *)
%Y A334000 Cf. A004041.
%K A334000 nonn,easy
%O A334000 0,3
%A A334000 _Greg Huber_, Apr 11 2020