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 A071719 #13 Oct 23 2019 10:07:26
%S A071719 1,4,15,53,185,647,2277,8073,28834,103700,375326,1366290,4999717,
%T A071719 18382405,67877025,251615745,936047790,3493585920,13077995730,
%U A071719 49091198550,184742369370,696863109774,2634345976818,9978753842378
%N A071719 Expansion of (1+x^2*C)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%H A071719 Robert Israel, <a href="/A071719/b071719.txt">Table of n, a(n) for n = 0..1665</a>
%F A071719 Conjecture: -3*(n+4)*(3*n-1)*a(n) +5*(n+2)*(7*n+3)*a(n-1) +2*(2*n-3)*(n-7)*a(n-2)=0. - _R. J. Mathar_, Aug 25 2013
%F A071719 Conjecture confirmed using the differential equation (4*x^4+35*x^3-9*x^2)*g'' + (-14*x^3+190*x^2-42*x)*g' + (-10*x^2+150*x+12)*g = 30*x+12 satisfied by the G.f. - _Robert Israel_, Jun 07 2018
%F A071719 a(n) ~ 37 * 4^n / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Oct 23 2019
%p A071719 f:= gfun:-rectoproc({-3*(n+4)*(3*n-1)*a(n) +5*(n+2)*(7*n+3)*a(n-1) +2*(2*n-3)*(n-7)*a(n-2)=0,a(0)=1,a(1)=4},a(n),remember):
%p A071719 map(f, [$0..40]); # _Robert Israel_, Jun 07 2018
%t A071719 (1 + c x^2) c^4 /. c -> (1 - (1 - 4x)^(1/2))/(2x) + O[x]^24 // CoefficientList[#, x]& (* _Jean-François Alcover_, Oct 23 2019 *)
%K A071719 nonn
%O A071719 0,2
%A A071719 _N. J. A. Sloane_, Jun 06 2002