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 A190725 #16 Mar 27 2017 03:53:56
%S A190725 1,3,14,69,355,1872,10037,54459,298138,1643565,9111191,50739120,
%T A190725 283635481,1590648819,8945090870,50423423685,284831065723,
%U A190725 1611918320688,9137141645645,51869777201595,294843392318146,1677980087882013,9559901907126959
%N A190725 Diagonal sums of Riordan matrix A118384.
%H A190725 Vincenzo Librandi, <a href="/A190725/b190725.txt">Table of n, a(n) for n = 0..200</a>
%F A190725 a(n) = (3*sum((-1)^k*F(2k+1)*d(n-k),k=0..n)-(-1)^n*F(2n+2))/2, where d(n) = central Delannoy number (A001850) and F(n) = Fibonacci number (A000045).
%F A190725 G.f.: (3+3*x-sqrt(1-6*x+x^2))/(2*(1+3*x+x^2)*sqrt(1-6*x+x^2)).
%F A190725 Recurrence: (n^2+11*n+30)*a(n+6)-(3*n^2+29*n+70)*a(n+5)-(17*n^2+177*n+458)*a(n+4)-34*(n+4)*a(n+3)+(17*n^2+95*n+130)*a(n+2)+(3*n^2+19*n+30)*a(n+1)-(n^2+5*n+6)*a(n)=0.
%F A190725 conjecture: n*(2*n-3)*a(n) +(-6*n^2+15*n-8)*a(n-1) +2*(-16*n^2+32*n-11)*a(n-2) +(-6*n^2+9*n-2)*a(n-3) +(2*n-1)*(n-2)*a(n-4) =0. - _R. J. Mathar_, Jul 24 2012
%F A190725 a(n) ~ sqrt(24+17*sqrt(2))*(3+2*sqrt(2))^n/(6*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 24 2012
%t A190725 CoefficientList[Series[(3+3x-Sqrt[1-6x+x^2])/(2(1+3x+x^2)Sqrt[1-6x+x^2]),{x,0,100}],x]
%o A190725 (PARI) x='x+O('x^50); Vec((3+3*x-sqrt(1-6*x+x^2))/(2*(1+3*x+x^2)*sqrt(1-6*x+x^2))) \\ _G. C. Greubel_, Mar 26 2017
%Y A190725 Cf. A000045, A001850, A118384.
%K A190725 nonn
%O A190725 0,2
%A A190725 _Emanuele Munarini_, May 17 2011