%I #6 Jan 28 2020 16:11:34
%S 1,1,6,71,1336,35233,1205605,50905881,2561801682,149816972193,
%T 9988787022964,748036456826960,62173668375158492,5679720951862607185,
%U 565666934647950245036,61000592050512159666215
%N Derived from the central terms (A127134) of triangle A127126; a(n) = A127126(2n,n)/(n+1).
%H G. C. Greubel, <a href="/A127135/b127135.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = A127134(n)/(n+1).
%t T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 +x*Sum[x^(r-k-1)*Sum[T[r, c], {c,k+1,r}], {r,k+1,n}] +x^(n+1))^(k+1), x, n-k]]; Table[T[2*n, n]/(n+1), {n, 0, 20}] (* _G. C. Greubel_, Jan 28 2020 *)
%Y Cf. A127126, A127127, A127128, A127129, A127130, A127131, A127132, A127133, A127134.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 05 2007