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 A216044 #15 Feb 14 2021 18:34:18
%S A216044 1,3,13,15,61,106,253,27545,62785,218107,1004593
%N A216044 Numbers k such that Sum_{j=1..k-1} (4j)!/16^j is an integer.
%C A216044 Next term > 1200000.
%t A216044 seq={}; sum=0; fak=1; k=0; While[k<10000, sum+=fak; If[Denominator[sum]==1, AppendTo[seq,k+1]]; k++; fak*=k*(4*k-1)*(4*k-2)*(4*k-3)/4;]; seq
%Y A216044 Cf. A215972, A216042, A216043, A216045.
%K A216044 nonn,more
%O A216044 1,2
%A A216044 _Vaclav Kotesovec_, Aug 30 2012