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 A128419 #22 Jan 30 2020 21:29:16
%S A128419 1,4,25,168,1181,8524,62609,465616,3495013,26423604,200920985,
%T A128419 1534936440,11771854381,90578698396,698921030945,5406132020128,
%U A128419 41905249405301,325434733291396,2531523208218665,19721766268370248,153847524455503421,1201601094053039596,9395224234956935345
%N A128419 Expansion of 8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7)).
%C A128419 Diagonal sums of number triangle A128417.
%H A128419 Vincenzo Librandi, <a href="/A128419/b128419.txt">Table of n, a(n) for n = 0..300</a>
%F A128419 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k)*C(2n-2k,n-2k).
%F A128419 D-finite with recurrence: 3*n*(15*n-22)*a(n) = 4*(75*n^2-155*n+63)*a(n-1) + (465*n^2-922*n+336)*a(n-2) + 4*(2*n-3)*(15*n-7)*a(n-3) . - _Vaclav Kotesovec_, Oct 20 2012
%F A128419 a(n) ~ 2^(3*n+4)/(15*sqrt(Pi*n)) . - _Vaclav Kotesovec_, Oct 20 2012
%t A128419 CoefficientList[Series[8/(Sqrt[1-8x](Sqrt[1-8x]+4x+7)),{x,0,30}],x] (* _Harvey P. Dale_, Apr 24 2012 *)
%t A128419 Table[Sum[2^(n-2*k)*Binomial[2*n-2*k,n-2*k], {k,0,Floor[n/2]}],{n,0,50}] (* _G. C. Greubel_, Feb 09 2017 *)
%o A128419 (PARI) x='x+O('x^50); Vec(8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7))) \\ _G. C. Greubel_, Feb 09 2017
%K A128419 easy,nonn
%O A128419 0,2
%A A128419 _Paul Barry_, Mar 02 2007