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 A259239 #18 Jan 30 2020 04:34:53
%S A259239 1,1,2,4,13,41,211,967,7274,44578,449551,3456641,43883797,405589549,
%T A259239 6212792678,67022223556,1202604514141,14825243365517,304950638503279,
%U A259239 4227716923246963,98067246206824406,1509933505953992386,38990856819985996927,660048542856323263589,18778057160849966289433
%N A259239 E.g.f.: exp(x-sqrt(1-x^2)+1).
%H A259239 Alois P. Heinz, <a href="/A259239/b259239.txt">Table of n, a(n) for n = 0..450</a>
%F A259239 a(n) ~ (exp(2) + (-1)^n) * n^(n-1) / exp(n). - _Vaclav Kotesovec_, Jun 22 2015
%F A259239 a(n) = ((2*n-3)*a(n-1) + (n-1)*(n^2-5*n+5)*a(n-2) + 2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2) for n >= 4. - _Alois P. Heinz_, Jan 30 2020
%p A259239 a:= proc(n) option remember; `if`(n<4, [1$2, 2, 4][n+1],
%p A259239 ((2*n-3)*a(n-1) +(n-1)*(n^2-5*n+5)*a(n-2)
%p A259239 +2*(n-1)*(n-2)*(n-3)*(a(n-4)-a(n-3)))/(n-2))
%p A259239 end:
%p A259239 seq(a(n), n=0..25); # _Alois P. Heinz_, Jun 22 2015
%t A259239 CoefficientList[Series[E^(x-Sqrt[1-x^2]+1), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jun 22 2015 *)
%K A259239 nonn
%O A259239 0,3
%A A259239 _Karol A. Penson_, Jun 22 2015