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 A081920 #10 Feb 19 2018 22:03:35
%S A081920 1,2,5,14,49,202,1069,6470,48353,391058,3767029,37936318,445650385,
%T A081920 5359634906,74198053661,1036667808758,16516851030721,262805595346210,
%U A081920 4735033850606437,84510767762583662,1698609728377283441
%N A081920 Expansion of exp(2x)/sqrt(1-x^2).
%C A081920 Binomial transform of A081919
%H A081920 Robert Israel, <a href="/A081920/b081920.txt">Table of n, a(n) for n = 0..449</a>
%F A081920 E.g.f. exp(2x)/sqrt(1-x^2).
%F A081920 Conjecture: a(n) -2*a(n-1) -(n-1)^2*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Nov 24 2012
%F A081920 Conjecture confirmed using d.e. (x^2-1)*y' + (-2*x^2+x+2)*y = 0 satisfied by the E.g.f. - _Robert Israel_, Feb 19 2018
%F A081920 a(n) ~ n^n * (exp(2)+(-1)^n*exp(-2)) / exp(n). - _Vaclav Kotesovec_, Feb 04 2014
%p A081920 f:= gfun:-rectoproc({a(n) -2*a(n-1) -(n-1)^2*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0, a(0)=1,a(1)=2,a(2)=5},a(n),remember):
%p A081920 map(f, [$0..30]); # _Robert Israel_, Feb 19 2018
%t A081920 CoefficientList[Series[E^(2*x)/Sqrt[1-x^2], {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Feb 04 2014 *)
%Y A081920 Cf. A081921.
%K A081920 easy,nonn
%O A081920 0,2
%A A081920 _Paul Barry_, Apr 01 2003