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 A213782 #20 Oct 17 2016 10:16:40
%S A213782 1,7,19,41,72,118,176,254,347,465,601,767,954,1176,1422,1708,2021,
%T A213782 2379,2767,3205,3676,4202,4764,5386,6047,6773,7541,8379,9262,10220,
%U A213782 11226,12312,13449,14671,15947,17313,18736,20254,21832,23510,25251,27097,29009,31031
%N A213782 Principal diagonal of the convolution array A213781.
%H A213782 Clark Kimberling, <a href="/A213782/b213782.txt">Table of n, a(n) for n = 1..1000</a>
%H A213782 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A213782 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A213782 G.f.: x*(1+5*x+4*x^2-2*x^4) / ((1-x)^4*(1+x)^2). - Corrected by _Colin Barker_, Jan 31 2016
%F A213782 From _Colin Barker_, Jan 31 2016: (Start)
%F A213782 a(n) = (16*n^3+66*n^2+6*(-1)^n*n-34*n-3*(-1)^n+3)/48.
%F A213782 a(n) = (8*n^3+33*n^2-14*n)/24 for n even.
%F A213782 a(n) = (8*n^3+33*n^2-20*n+3)/24 for n odd.
%F A213782 (End)
%t A213782 (See A213781.)
%t A213782 LinearRecurrence[{2,1,-4,1,2,-1},{1,7,19,41,72,118},50] (* _Harvey P. Dale_, Oct 17 2016 *)
%o A213782 (PARI) Vec(x*(1+5*x+4*x^2-2*x^4)/((1-x)^4*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jan 31 2016
%Y A213782 Cf. A213781, A213500.
%K A213782 nonn,easy
%O A213782 1,2
%A A213782 _Clark Kimberling_, Jun 22 2012