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 A270715 #13 Dec 12 2023 18:51:04
%S A270715 1,3,5,10,19,35,65,120,221,407,749,1378,2535,4663,8577,15776,29017,
%T A270715 53371,98165,180554,332091,610811,1123457,2066360,3800629,6990447,
%U A270715 12857437,23648514,43496399,80002351,147147265
%N A270715 a(n) = ((n+2)/2)*Sum_{k=0..n/2}(Sum_{i=0..n-2*k} binomial(k+1,n-2*k-i)*binomial(k+i,k))/(k+1).
%H A270715 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, 0, -1).
%F A270715 G.f.: (-x^2+x+1)/((1-x)*(-x^3-x^2-x+1)).
%t A270715 LinearRecurrence[{2,0,0,-1},{1,3,5,10},40] (* _Harvey P. Dale_, May 23 2017 *)
%o A270715 (Maxima)
%o A270715 a(n):=(n+2)/2*(sum(sum(binomial(k+1,n-2*k-i)*binomial(k+i,k),i,0,n-2*k)/(k+1),k,0,n/2));
%o A270715 (PARI) x='x+O('x^200); Vec((-x^2+x+1)/((1-x)*(-x^3-x^2-x+1))) \\ _Altug Alkan_, Mar 22 2016
%Y A270715 Cf. A113413, A270709.
%K A270715 nonn
%O A270715 0,2
%A A270715 _Vladimir Kruchinin_, Mar 22 2016