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 A116394 #13 Sep 08 2022 08:45:24
%S A116394 1,1,4,11,33,100,305,937,2890,8943,27741,86216,268355,836297,2608818,
%T A116394 8144875,25446229,79545148,248780979,778400001,2436380402,7628211951,
%U A116394 23890103153,74836927720,234478937321,734802907841,2303073316042
%N A116394 Expansion of 1/((1+x)*sqrt(1-2*x-3*x^2) - x).
%H A116394 G. C. Greubel, <a href="/A116394/b116394.txt">Table of n, a(n) for n = 0..1000</a>
%F A116394 a(n) = Sum_{k=0..floor(n/2)} A116392(n-k,k).
%F A116394 D-finite with recurrence: n*a(n) +2*(-n+1)*a(n-1) +2*(-5*n+6)*a(n-2) +2*(3*n-7)*a(n-3) +2*(17*n-50)*a(n-4) +6*(5*n-17)*a(n-5) +9*(n-4)*a(n-6)=0. - _R. J. Mathar_, Jan 23 2020
%t A116394 CoefficientList[Series[1/((1+x)*Sqrt[1-2x-3x^2] -x), {x, 0, 30}], x] (* _G. C. Greubel_, May 28 2019 *)
%o A116394 (PARI) my(x='x+O('x^30)); Vec(1/((1+x)*sqrt(1-2*x-3*x^2) - x)) \\ _G. C. Greubel_, May 28 2019
%o A116394 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/((1+x)*Sqrt(1-2*x-3*x^2) - x) )); // _G. C. Greubel_, May 28 2019
%o A116394 (Sage) (1/((1+x)*sqrt(1-2*x-3*x^2) - x)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019
%Y A116394 Diagonal sums of number triangle A116392.
%K A116394 easy,nonn
%O A116394 0,3
%A A116394 _Paul Barry_, Feb 12 2006