%I #11 May 16 2012 08:50:35
%S 1,2,3,7,21,51,138,358,969,2735,7514,21372,60144,171510,485294,
%T 1388586,3949211,11296953,32294750,92471813,265484354,762548923,
%U 2194099432,6318266076,18214160616,52525201261,151638570041,437959067720,1265890334086,3661612407681
%N Row square-sums of triangle A096815.
%t T[n_,k_] := T[n,k] = If[n < k || k < 0, 0, If[k = 1 || k == n, 1, Sum[T[n-k,j]T[k,k-j],{j,0,k}]]]
%t Table[Sum[T[n,k]^2,{k,0,n}],{n,0,50}]
%o (Maxima) T(n,k):= if ( n<k or k<0 ) then 0 else
%o if ( k<=1 or k=n ) then 1 else sum(T(n-k,j)*T(k,k-j),j,0, k);
%o makelist(sum(T(n,k)^2,k,0,n),n,0,20);
%Y Cf. A096815, A096816, A212264, A212421, A212422.
%K nonn
%O 0,2
%A _Emanuele Munarini_, May 12 2012