%I #7 Jan 30 2020 22:03:48
%S 1,1,5,48,727,15455,428338,14732200,607324669,29250572599,
%T 1614093015100,100494752982578,6973042276811149,533791252851029495,
%U 44701948131110427743,4066190846579443681053,399302066160095572863595
%N Derived from central terms (A127090) of triangle A127082; a(n) = A127090(n)/(n+1).
%H G. C. Greubel, <a href="/A127091/b127091.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = A127082(2*n,n)/(n+1).
%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+1), {n, 0, 15}] (* _G. C. Greubel_, Jan 30 2020 *)
%Y Cf. A127082, A127083, A127084, A127085, A127086, A127087, A127088, A127089, A127090.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 04 2007