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 A239425 #26 Nov 08 2024 07:23:34
%S A239425 1,2,7,16,53,156,522,1702,5833,19990,70079,247160,882587,3172196,
%T A239425 11492847,41874864,153452521,564975570,2089346157,7756501690,
%U A239425 28898156364,108010059036,404890987653,1521877280868,5734545323859,21657665796526
%N A239425 Expansion of -16/(sqrt(12*x+2*sqrt(1-4*x)+2)-sqrt(1-4*x)-1)^2+1/x^2-1.
%H A239425 G. C. Greubel, <a href="/A239425/b239425.txt">Table of n, a(n) for n = 0..1000</a>
%F A239425 a(n) = (Sum_{j=0..(n+2)} C(n+2*j-1,j)*(-1)^(j+n)*C(2*n+2,j+n))/(n+1) - delta(n,0).
%F A239425 a(n) ~ (5+3*sqrt(5)) * 2^(2*n+1) / (5*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Mar 18 2014
%F A239425 Conjecture: 2*(2*n+1)*(n+2)*(n+1)*a(n) +(n+1)*(n^2-27*n+2)*a(n-1) +2*(-73*n^3+204*n^2-167*n+6)*a(n-2) +12*(n-3)*(2*n-3)*(4*n-7)*a(n-3) +216*(2*n-5)*(n-3)*(2*n-3)*a(n-4)=0. - _R. J. Mathar_, Apr 02 2014
%t A239425 CoefficientList[Series[-16/(Sqrt[12*x+2*Sqrt[1-4*x]+2]-Sqrt[1-4*x] -1)^2+1/x^2-1, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 18 2014 *)
%t A239425 Flatten[{1,Table[Sum[Binomial[n+2*j-1,j+n-1]*(-1)^(j+n)*Binomial[2*n+2,j+n],{j,0,n+2}]/(n+1),{n,1,20}]}] (* _Vaclav Kotesovec_, Mar 18 2014 *)
%o A239425 (Maxima)
%o A239425 a(n):=(sum(binomial(n+2*j-1, j)*(-1)^(j+n)*binomial(2*n+2, j+n), j, 0, n+2))/(n+1)-kron_delta(n,0);
%o A239425 (PARI) my(x='x+O('x^50)); Vec(-16/(sqrt(12*x+2*sqrt(1-4*x)+2)-sqrt(1-4*x) -1)^2 + 1/x^2 -1) \\ _G. C. Greubel_, Jun 01 2017
%Y A239425 Cf. A097609, A055113.
%K A239425 nonn
%O A239425 0,2
%A A239425 _Vladimir Kruchinin_, Mar 17 2014