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 A213843 #19 Sep 08 2022 08:46:02
%S A213843 1,13,62,190,455,931,1708,2892,4605,6985,10186,14378,19747,26495,
%T A213843 34840,45016,57273,71877,89110,109270,132671,159643,190532,225700,
%U A213843 265525,310401,360738,416962,479515,548855,625456,709808,802417,903805,1014510
%N A213843 Antidiagonal sums of the convolution array A213841.
%H A213843 Clark Kimberling, <a href="/A213843/b213843.txt">Table of n, a(n) for n = 1..1000</a>
%H A213843 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A213843 a(n) = n*(1 + n)*(1 - 2*n + 4*n^2)/6.
%F A213843 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A213843 G.f.: f(x)/g(x), where f(x) = x*(1 + x)(1 + 8*x) and g(x) = (1-x)^5.
%p A213843 A213843:=n->n*(1 + n)*(1 - 2*n + 4*n^2)/6: seq(A213843(n), n=1..30); # _Wesley Ivan Hurt_, Oct 09 2014
%t A213843 Table[n (1 + n) (1 - 2 n + 4 n^2)/6, {n, 30}] (* _Wesley Ivan Hurt_, Oct 09 2014 *)
%o A213843 (Magma) [n*(1 + n)*(1 - 2*n + 4*n^2)/6 : n in [1..30]]; // _Wesley Ivan Hurt_, Oct 09 2014
%Y A213843 Cf. A213841.
%K A213843 nonn,easy
%O A213843 1,2
%A A213843 _Clark Kimberling_, Jul 05 2012