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%I #10 May 16 2012 03:00:09
%S 1,2,3,5,9,15,26,44,75,129,220,378,648,1114,1910,3284,5635,9677,16608,
%T 28501,48930,83973,144150,247396,424612,728577,1250185,2144858,
%U 3679772,6313029,10830673,18581706,31880471,54698330,93847987,161021223
%N Row sums of triangle A096815, in which A096815(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and k.
%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], {k, 0, n}], {n, 0, 50}] [Emanuele Munarini, May 16 2012]
%o (Maxima) T(n,k):= if ( n<k or k<0 ) then 0 else 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),k,0,n),n,0,12); [Emanuele Munarini, May 12 2012]
%Y Cf. A096815.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 20 2004
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