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 A036243 #34 Aug 18 2024 23:03:46
%S A036243 1,2,9,56,457,4626,55969,788192,12667041,228794930,4588565641,
%T A036243 101177239032,2432842302409,63355077101666,1776375001149057,
%U A036243 53354605111573376,1709123738571497089,58163561716542474402,2095597345534100575561
%N A036243 Denominator of fraction equal to the continued fraction [ 0, 2, 4, ...2n ].
%F A036243 a(n) = b(n+1) where b(n) = K(n,1)*I(0,1) - (-1)^n*I(n,1)*K(0,1), K(n,x) and I(n,x) Bessel functions. - _Peter Luschny_, Sep 14 2014
%F A036243 a(n) = Sum_{0..n} |A369585(n)|. - _Peter Luschny_, Jan 30 2024
%F A036243 a(n) = 2*n*a(n-1) + a(n-2). - _Christian Krause_, Aug 18 2024
%p A036243 b := n -> BesselK(n,1)*BesselI(0,1)-(-1)^n*BesselI(n,1)* BesselK(0,1);
%p A036243 A036243 := n -> b(n+1):
%p A036243 seq(simplify(A036243(n)), n=0..18); # _Peter Luschny_, Sep 14 2014
%t A036243 Table[Denominator[FromContinuedFraction[Range[0,2n,2]]],{n,0,20}] (* _Harvey P. Dale_, Feb 18 2016 *)
%o A036243 (PARI) a(n)=contfracpnqn(vector(n+1,i,2*i-2))[2,1];
%o A036243 vector(22,n,a(n-1)) \\ _M. F. Hasler_, Feb 08 2011; edited by _Michel Marcus_, Feb 12 2024
%Y A036243 Cf. A036242 (numerator), A369585.
%K A036243 frac,nonn
%O A036243 0,2
%A A036243 _Jeff Burch_
%E A036243 a(0) = 1 prepended by _Peter Luschny_, Jan 30 2024