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 A208658 #14 Nov 22 2023 22:29:23
%S A208658 0,4,17,52,139,346,825,1912,4343,9718,21493,47092,102387,221170,
%T A208658 475121,1015792,2162671,4587502,9699309,20447212,42991595,90177514,
%U A208658 188743657,394264552,822083559,1711276006,3556769765,7381975012
%N A208658 Row sums of A208657.
%H A208658 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A208658 Conjectures from _Colin Barker_, Mar 20 2012: (Start)
%F A208658 a(n) = -2^(-1+n)+(-1+2^n)*n.
%F A208658 G.f.: x^2*(4-7*x+2*x^2)/((1-x)^2*(1-2*x)^2). (End)
%F A208658 From _Stefano Spezia_, Nov 19 2023: (Start)
%F A208658 The above conjectures are true.
%F A208658 E.g.f.: exp(x)*(exp(x)*(4*x - 1) - 2*x)/2. (End)
%t A208658 f[n_, k_] := n*Binomial[n, k] - Binomial[n - 1, k - 1]
%t A208658 Table[Sum[f[n, k], {k, 1, n}], {n, 1, 3 z}](* A208658 *)
%Y A208658 Cf. A208657.
%K A208658 nonn,easy
%O A208658 1,2
%A A208658 _Clark Kimberling_, Mar 01 2012