%I #9 Jan 28 2020 08:37:29
%S 1,1,3,13,77,587,5484,60582,771261,11102828,178144861,3149976426,
%T 60825085447,1273060083700,28700081677767,693217471426114,
%U 17857152401368800,488620956679818191,14152040894854881662,432509671322583878614,13908794132963653028146
%N Column 0 of triangle A127126.
%C For n > 0, equals one-half of the row sums of triangle A127126.
%H G. C. Greubel, <a href="/A127127/b127127.txt">Table of n, a(n) for n = 0..80</a>
%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[n, 0], {n, 0, 20}] (* _G. C. Greubel_, Jan 28 2020 *)
%Y Cf. A127126, A127128, A127129, A127130, A127131, A127132, A127133, A127134, A127135.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 05 2007