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 A197209 #22 Jan 09 2021 11:05:54
%S A197209 3,24,180,1320,9660,70896,522648,3871440,28809990,215318400,
%T A197209 1615579680,12165491520,91905439080,696359055840,5290416835440,
%U A197209 40291036122528,307537305284574,2352216447006480,18024996856976760
%N A197209 Row sums of A197208.
%H A197209 Seiichi Manyama, <a href="/A197209/b197209.txt">Table of n, a(n) for n = 2..1000</a>
%F A197209 For n >= 2, a(n) = Sum_{k = 1..n-1} C(n-1,k-1)*C(n,k+1)*C(n+1,k), where C(n,k) = binomial(n,k).
%F A197209 a(n) = (1/(n+2)) * ((7*n^2-7*n-2)*a(n-1)/(n-2) + 8*n*a(n-2)) for n > 3. - _Seiichi Manyama_, Jan 09 2021
%t A197209 Table[Sum[Binomial[n-1,k-1]Binomial[n,k+1]Binomial[n+1,k],{k,n-1}],{n,2,20}] (* _Harvey P. Dale_, May 08 2016 *)
%o A197209 (PARI) a(n) = sum(k=1, n-1, binomial(n-1,k-1)*binomial(n,k+1)*binomial(n+1,k)); \\ _Michel Marcus_, Jan 09 2021
%Y A197209 Cf. A007318, A197208.
%K A197209 nonn,easy
%O A197209 2,1
%A A197209 _Peter Bala_, Oct 12 2011