%I A104445
%S A104445 1,1,1,1,1,1,1,2,1,1,1,4,3,1,1,1,9,9,4,1,1,1,24,30,16,5,1,1,1,77,115,70,
%T A104445 25,6,1,1,1,295,510,344,135,36,7,1,1,1,1329,2602,1908,805,231,49,8,1,1,
%U A104445 1,6934,15133,11904,5325,1616,364,64,9,1,1,1,41351,99367,83028,39001
%N A104445 Triangular matrix T, read by rows, that satisfies: SHIFT_LEFT_UP(T) = 
               T^2 - T + I, or, equivalently: T(n+1,k+1) = [T^2](n,k) - T(n,k) + 
               [T^0](n,k) for n>=k>=0, with T(0,0)=1.
%C A104445 Surprisingly, SHIFT_UP(T) = A091351, or T(n+1,k) = A091351(n,k) for n>
               =k>=0, where column k of A091351 equals column 0 of A091351^(k+1) 
               for k>=0.
%F A104445 T(n, k) = Sum_{j=0..n-k-1} T(n-k, j)*T(j+k, k-1) for n>k>0 with T(n, 
               0)=T(n, n)=1 (n>=0).
%e A104445 Rows begin:
%e A104445 1;
%e A104445 1,1;
%e A104445 1,1,1;
%e A104445 1,2,1,1;
%e A104445 1,4,3,1,1;
%e A104445 1,9,9,4,1,1;
%e A104445 1,24,30,16,5,1,1;
%e A104445 1,77,115,70,25,6,1,1;
%e A104445 1,295,510,344,135,36,7,1,1;
%e A104445 1,1329,2602,1908,805,231,49,8,1,1;
%e A104445 1,6934,15133,11904,5325,1616,364,64,9,1,1; ...
%o A104445 (PARI) {T(n,k)=if(n<k|k<0,0,if(n==k|k==0,1, sum(j=0,n-k-1,T(n-k,j)*T(j+k,
               k-1))))}
%Y A104445 Cf. A091351, A104446 (matrix square); columns form: A091352, A091353, 
               A091354.
%Y A104445 Sequence in context: A131508 A140130 A125653 this_sequence A000189 A000190 
               A003557
%Y A104445 Adjacent sequences: A104442 A104443 A104444 this_sequence A104446 A104447 
               A104448
%K A104445 nonn,tabl
%O A104445 0,8
%A A104445 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 07 2005