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 A137360 #12 May 31 2017 10:33:20
%S A137360 0,0,0,0,0,0,1,5,15,35,70,128,226,402,735,1375,2588,4830,8882,16108,
%T A137360 28943,51785,92573,165525,295869,528069,940259,1669725,2957941,
%U A137360 5229953,9233748,16284106,28688451,50490125,88765885,155891305,273495479,479360847,839451764
%N A137360 a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k+1).
%D A137360 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H A137360 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 8, -7, 6, -2, 0, -1).
%F A137360 G.f.: x^6*(1-x)/(x^5+x^3-3*x^2+3*x-1)^2. - _Alois P. Heinz_, Oct 23 2008
%p A137360 a:= n-> (Matrix([[35, 15, 5, 1, 0$6]]). Matrix (10, (i,j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1,10]: seq (a(n), n=0..50); # _Alois P. Heinz_, Oct 23 2008
%t A137360 Table[Sum[k Binomial[n-2k,3k+1],{k,n/2}],{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,8,-7,6,-2,0,-1},{0,0,0,0,0,0,1,5,15,35},40] (* _Harvey P. Dale_, May 31 2017 *)
%Y A137360 Cf. A137356-A137361, A136444.
%K A137360 nonn
%O A137360 0,8
%A A137360 _Don Knuth_, Apr 11 2008