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