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 A166359 #13 Aug 18 2018 08:33:35
%S A166359 1,3,15,197,6909,459383,48252699,7299708105,1499523879481,
%T A166359 401147660278507,135421121289695655,56285769483090611085,
%U A166359 28237152577765405343285,16821061018350834178553055
%N A166359 Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357.
%C A166359 Aeration of this sequence gives the diagonal sums of A166357.
%H A166359 Andrew Howroyd, <a href="/A166359/b166359.txt">Table of n, a(n) for n = 0..100</a>
%F A166359 a(n) = Sum_{k=0..n} C(n+k,2k)*A166356(k).
%F A166359 a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / exp(2*n). - _Vaclav Kotesovec_, Aug 17 2018
%t A166359 Table[1 + Sum[Binomial[n + k, 2*k] * ((2*k-1)! + (2*k-2)!), {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 17 2018 *)
%o A166359 (PARI) a(n)={1 + sum(k=1, n, binomial(n + k, 2*k) * ((2*k-1)! + (2*k-2)!))} \\ _Andrew Howroyd_, Aug 17 2018
%Y A166359 Cf. A166356, A166357.
%K A166359 easy,nonn
%O A166359 0,2
%A A166359 _Paul Barry_, Oct 12 2009