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A098446 Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the (n-1)-th diagonal with the k-th row of this triangle.

%I A098446 #7 Jun 13 2017 22:11:32
%S A098446 1,1,1,1,2,1,1,3,4,1,1,4,9,9,1,1,5,16,30,24,1,1,6,25,70,115,77,1,1,7,
%T A098446 36,135,344,510,295,1,1,8,49,231,805,1908,2602,1329,1,1,9,64,364,1616,
%U A098446 5325,11904,15133,6934,1,1,10,81,540,2919,12381,39001,83028,99367,41351,1
%N A098446 Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the (n-1)-th diagonal with the k-th row of this triangle.
%C A098446 The rows of this triangle are the reverse of the rows of triangle A091351, in which the k-th column lists the row sums of the k-th matrix power of A091351. Row sums form A091352 and equal the secondary diagonal.
%F A098446 T(n, k) = Sum_{i=0..k} T(k, i)*T(n-i-1, k-i) for 0<k<n, else T(0, n)=T(n, n)=1.
%e A098446 T(7,3) = T(3,0)*T(6,3) + T(3,1)*T(5,2) + T(3,2)*T(4,1) + T(3,3)*T(3,0)
%e A098446 = 1*70 + 3*16 + 4*4 + 1*1 = 135.
%e A098446 Rows begin:
%e A098446 [1],
%e A098446 [1,1],
%e A098446 [1,2,1],
%e A098446 [1,3,4,1],
%e A098446 [1,4,9,9,1],
%e A098446 [1,5,16,30,24,1],
%e A098446 [1,6,25,70,115,77,1],
%e A098446 [1,7,36,135,344,510,295,1],
%e A098446 [1,8,49,231,805,1908,2602,1329,1],
%e A098446 [1,9,64,364,1616,5325,11904,15133,6934,1],...
%o A098446 (PARI) T(n,k)=if(n<k || k<0,0,if(n==k || k==0,1,sum(i=0,k,T(k,i)*T(n-i-1,k-i));))
%Y A098446 Cf. A091351, A091352.
%K A098446 nonn,tabl
%O A098446 0,5
%A A098446 _Paul D. Hanna_, Sep 07 2004