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 A103978 #28 Aug 06 2022 14:15:50
%S A103978 1,3,6,9,54,54,540,405,5670,3402,61236,30618,673596,288684,7505784,
%T A103978 2814669,84440070,28146690,956987460,287096238,10909657044,2975361012,
%U A103978 124965162504,31241290626,1437099368796,331638315876,16581915793800
%N A103978 Expansion of (sqrt(1-12*x^2)+12*x^2+2*x-1)/(2*x*sqrt(1-12*x^2)).
%H A103978 Robert Israel, <a href="/A103978/b103978.txt">Table of n, a(n) for n = 0..1855</a>
%F A103978 G.f.: 1/sqrt(1-12*x^2)+(1-sqrt(1-12*x^2))/(2*x).
%F A103978 a(n) = sum{k=0..floor(n/2), 3^(n-k) * A000108(k) * C(k+1, n-k)}.
%F A103978 D-finite with recurrence: -(n+1)*a(n)+2*(n-1)*a(n-1) +12*(2n-3)*a(n-2) +24(2-n)*a(n-3) + 144*(4-n)*a(n-4)=0. - _R. J. Mathar_, Dec 14 2011
%F A103978 a(n) ~ 2^(n + 1/2) * 3^(n/2) / sqrt(Pi*n) if n is even and a(n) ~ 2^(n + 1/2) * 3^((n+1)/2) / (sqrt(Pi) * n^(3/2)) if n is odd. - _Vaclav Kotesovec_, Nov 19 2021
%p A103978 rec:= -(n+1)*a(n)+2*(n-1)*a(n-1)+12*(2*n-3)*a(n-2)+24*(2-n)*a(n-3)+144*(4-n)*a(n-4):
%p A103978 f:= gfun:-rectoproc({rec=0,a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 9},a(n),remember):
%p A103978 map(f, [$0..30]); # _Robert Israel_, Sep 13 2020
%t A103978 CoefficientList[Series[(Sqrt[1-12x^2]+12x^2+2x-1)/(2x Sqrt[1-12x^2]),{x,0,30}],x] (* _Harvey P. Dale_, Aug 06 2022 *)
%Y A103978 Cf. A025225, A059304, A103973.
%K A103978 easy,nonn
%O A103978 0,2
%A A103978 _Paul Barry_, Feb 23 2005