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%I #11 Jun 13 2017 22:09:59
%S 1,1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,4,4,4,1,1,1,5,6,7,5,1,1,1,6,9,11,9,
%T 6,1,1,1,7,11,17,17,13,7,1,1,1,8,14,24,30,26,16,8,1,1,1,9,18,32,42,50,
%U 36,21,9,1,1,1,10,21,42,61,79,76,51,25,10,1,1,1,11,25,53,85,118,129,115,67
%N Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and k.
%C Row sums are A096816.
%F T(n, k) = Sum_{j=0..min(n-k, k)} T(n-k, j)*T(k, k-j), for n>=k>=1, with T(n, 0)=T(n+1, 1)=T(n, n)=1 for n>=0.
%e T(7,4) = 11 = 4th term of the convolution of row (7-4) and row 4:
%e T(3,0)*T(4,4) + T(3,1)*T(4,3) + T(3,2)*T(4,2) + T(3,3)*T(4,1).
%e Rows begin:
%e [1],
%e [1,1],
%e [1,1,1],
%e [1,1,2,1],
%e [1,1,3,3,1],
%e [1,1,4,4,4,1],
%e [1,1,5,6,7,5,1],
%e [1,1,6,9,11,9,6,1],
%e [1,1,7,11,17,17,13,7,1],
%e [1,1,8,14,24,30,26,16,8,1],
%e [1,1,9,18,32,42,50,36,21,9,1],
%e [1,1,10,21,42,61,79,76,51,25,10,1],
%e [1,1,11,25,53,85,118,129,115,67,31,11,1],...
%o (PARI) T(n,k)=if(n<k || k<0,0,if(k<=1 || k==n,1,sum(j=0,k,T(n-k,j)*T(k,k-j))))
%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 create_list(T(n,k),n,0,12,k,0,n); /* _Emanuele Munarini_, May 12 2012 */
%Y Cf. A096816, A096811.
%K nonn,tabl
%O 0,9
%A _Paul D. Hanna_, Jul 20 2004
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