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 A212205 #16 Jan 30 2020 21:29:17
%S A212205 1,1,2,4,8,18,36,86,172,426,852,2162,4324,11166,22332,58438,116876,
%T A212205 309042,618084,1648154,3296308,8851206,17702412,47813790,95627580,
%U A212205 259585002,519170004,1415431266,2830862532,7747200558,15494401116,42545600310,85091200620,234346445154,468692890308,1294260644906,2588521289812,7165245015510,14330490031020
%N A212205 G.f.: ((1+2*x)*sqrt(1-6*x^2+x^4)-1+5*x^2-2*x^3)/(2*x*(1-6*x^2)).
%H A212205 Alois P. Heinz, <a href="/A212205/b212205.txt">Table of n, a(n) for n = 0..1000</a>
%H A212205 D. E. Davenport, L. W. Shapiro and L. C. Woodson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i2p33">The Double Riordan Group</a>, The Electronic Journal of Combinatorics, 18(2) (2012), #P33.
%F A212205 a(n) ~ 2*2^(3/4)*(1+sqrt(2))^(n+3)/(n^(3/2)*sqrt(Pi)) if n is even and a(n) ~ 2^(3/4)*(1+sqrt(2))^(n+4)/(n^(3/2)*sqrt(Pi)) if n is odd. - _Vaclav Kotesovec_, May 21 2013
%F A212205 Conjecture D-finite with recurrence: (n+1)*a(n) +2*(n-1)*a(n-1) +6*(-2*n+1)*a(n-2) +12*(-2*n+5)*a(n-3) +(37*n-77)*a(n-4) +2*(37*n-151)*a(n-5) +6*(-n+5)*a(n-6) +12*(-n+7)*a(n-7)=0. - _R. J. Mathar_, Aug 20 2018
%p A212205 a:= proc(n) option remember; `if`(n<6, [1, 1, 2, 4, 8, 18][n+1],
%p A212205 (-132*a(n-1) +(660-834*n+84*n^2)*a(n-2) +804*a(n-3)
%p A212205 +(2981*n-6690-259*n^2)*a(n-4) -72*a(n-5) +6*(n-6)*(7*n-59)*a(n-6))
%p A212205 / ((n+1)*(7*n-66)))
%p A212205 end:
%p A212205 seq(a(n), n=0..40); # _Alois P. Heinz_, May 21 2013
%t A212205 CoefficientList[Series[((1+2*x)*Sqrt[1-6*x^2+x^4]-1+5*x^2-2*x^3)/(2*x*(1-6*x^2)), {x, 0, 20}], x] (* _Vaclav Kotesovec_, May 21 2013 *)
%K A212205 nonn
%O A212205 0,3
%A A212205 _N. J. A. Sloane_, May 11 2012