A212264 - OEIS

%I #10 May 16 2012 03:03:49

%S 1,1,2,2,3,4,6,9,12,18,26,37,52,77,110,156,226,324,464,668,960,1370,

%T 1977,2834,4060,5832,8371,11993,17219,24695,35408,50837,72880,104619,

%U 150065,215343,308868,443380,635753,912581,1308771,1878238,2693939,3866059,5544795

%N Diagonal 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,k],{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,k),k,0,n/2),n,0,32);

%Y Cf. A096815, A096816.

%K nonn

%O 0,3

%A _Emanuele Munarini_, May 12 2012