%I #6 Jan 30 2020 22:03:41
%S 1,2,15,192,3635,92730,2998366,117857600,5465922021,292505725990,
%T 17755023166100,1205937035790936,90649549598544937,
%U 7473077539914412930,670529221966656416145,65059053545271098896848
%N Central terms of triangle A127082; a(n) = A127082(2*n,n).
%C a(n) is divisible by (n+1): a(n)/(n+1) = A127091(n).
%H G. C. Greubel, <a href="/A127090/b127090.txt">Table of n, a(n) for n = 0..50</a>
%t T[n_, k_]:= T[n, k]= If[k==n, 1, Coefficient[(1 + x*Sum[x^(r-k)*Sum[T[r, c], {c,k,r}], {r,k,n-1}] + x^(n+1))^(k+1), x, n-k]]; Table[T[2*n, n], {n,0,15}] (* _G. C. Greubel_, Jan 30 2020 *)
%Y Cf. A127082, A127083, A127084, A127085, A127086, A127087, A127088, A127089, A127091.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 04 2007