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 A213562 #12 Jun 17 2017 03:53:57
%S A213562 1,18,109,407,1152,2723,5670,10746,18939,31504,49995,76297,112658,
%T A213562 161721,226556,310692,418149,553470,721753,928683,1180564,1484351,
%U A213562 1847682,2278910,2787135,3382236,4074903,4876669,5799942,6858037
%N A213562 Principal diagonal of the convolution array A213561.
%H A213562 Clark Kimberling, <a href="/A213562/b213562.txt">Table of n, a(n) for n = 1..1000</a>
%H A213562 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A213562 a(n) = (4/15)*n^5 + (11/24)*n^4 + (1/4)*n^3 + (1/24)*n^2 - (1/16)*n.
%F A213562 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).
%F A213562 G.f.: x*(1 + 12*x + 16*x^2 + 3*x^3)/(1 - x)^6.
%t A213562 (See A213561.)
%t A213562 LinearRecurrence[{6,-15,20,-15,6,-1},{1,18,109,407,1152,2723},30] (* _Harvey P. Dale_, Nov 12 2014 *)
%Y A213562 Cf. A213561, A213500.
%K A213562 nonn,easy
%O A213562 1,2
%A A213562 _Clark Kimberling_, Jun 18 2012