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 A172010 #15 Mar 15 2022 03:07:25
%S A172010 1,26,2741,683870,315704418,234725594388,257237392999893,
%T A172010 390832857108454838,787178784737043042806,2031210797603911366282796,
%U A172010 6536955866068372922068141666,25676217636579568989377656129516,120915166829869713032692550819662756,672580820552232143302651758669053327784
%N A172010 a(n) = 2*A142458(2*n, n)/(n+1).
%H A172010 G. C. Greubel, <a href="/A172010/b172010.txt">Table of n, a(n) for n = 1..190</a>
%F A172010 a(n) = 2*A142458(2*n, n)/(n+1).
%t A172010 T[n_, k_, m_]:= T[n,k,m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1,k-1,m] + (m*k-m+ 1)*T[n-1,k,m]];
%t A172010 a[n_]:= 2*T[2*n,n,3]/(n+1);
%t A172010 Table[a[n], {n,30}] (* modified by _G. C. Greubel_, Mar 14 2022 *)
%o A172010 (Sage)
%o A172010 @CachedFunction
%o A172010 def T(n,k,m): # A142458
%o A172010 if (k==1 or k==n): return 1
%o A172010 else: return (m*(n-k)+1)*T(n-1,k-1,m) + (m*k-m+1)*T(n-1,k,m)
%o A172010 [2*T(2*n,n,3)/(n+1) for n in (1..30)] # _G. C. Greubel_, Mar 14 2022
%Y A172010 Cf. A142458, A177042, A177043.
%K A172010 nonn
%O A172010 1,2
%A A172010 _Roger L. Bagula_, Nov 19 2010
%E A172010 Name corrected and more terms added by _G. C. Greubel_, Mar 14 2022