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 A242019 #9 Aug 11 2014 10:52:37
%S A242019 1,1,33,3409,728575,265362370,147228369351,115651594418010,
%T A242019 122167455441632423,167035663137431205196,287018982366654934570328,
%U A242019 605456750773492887086145669,1538306721887736189212800143193,4633572348321634923252339927247392
%N A242019 a(n) = Sum_{k=0..n} Stirling2(2*n+k, k) * C(n, k).
%F A242019 a(n) ~ c * (r^4/((1-r)*(2*r-1)^2))^n * n^(2*n-1/2) / exp(2*n), where r = 0.949867370961706500554205072094811326960829788646... is the root of the equation (1-r)*(2+r)/r^2 = -LambertW(-exp(-1-2/r)*(2+r)/r), and c = 0.42307980713011095154197903821771057626302758607...
%t A242019 Table[Sum[Binomial[n,k] * StirlingS2[2*n+k,k],{k,0,n}],{n,0,20}]
%Y A242019 Cf. A243942, A218667.
%K A242019 nonn
%O A242019 0,3
%A A242019 _Vaclav Kotesovec_, Aug 11 2014