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 A213563 #12 Aug 10 2024 13:41:08
%S A213563 1,10,51,182,518,1260,2730,5412,9999,17446,29029,46410,71708,107576,
%T A213563 157284,224808,314925,433314,586663,782782,1030722,1340900,1725230,
%U A213563 2197260,2772315,3467646,4302585,5298706,6479992,7873008,9507080
%N A213563 Antidiagonal sums of the convolution array A213561.
%H A213563 Clark Kimberling, <a href="/A213563/b213563.txt">Table of n, a(n) for n = 1..1000</a>
%H A213563 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A213563 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F A213563 G.f.: x*(1 + 3 x + 2*x^2)/(1 - x)^7.
%t A213563 (See A213561.)
%t A213563 LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,10,51,182,518,1260,2730},40] (* _Harvey P. Dale_, Aug 10 2024 *)
%Y A213563 Cf. A213561, A213500.
%K A213563 nonn,easy
%O A213563 1,2
%A A213563 _Clark Kimberling_, Jun 18 2012