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A102320 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1).

%I A102320 #4 Mar 30 2012 18:36:44
%S A102320 1,1,3,4,9,5,33,72,25,7,436,945,300,49,9,8122,17568,5425,784,81,11,
%T A102320 197920,427770,130700,18081,1620,121,13,6007205,12979080,3947050,
%U A102320 535864,45441,2904,169,15,219413116,473981445,143812400,19348042,1599588,95953
%N A102320 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^2](n-1,k) when n>k>=0, with T(n,n) = (2*n+1).
%C A102320 Column 0 forms A102321. Column 1 forms A102322. The contribution of each term along the main diagonal to column 0 is given by triangle of coefficients A102323.
%e A102320 Rows of T begin:
%e A102320 [1],
%e A102320 [1,3],
%e A102320 [4,9,5],
%e A102320 [33,72,25,7],
%e A102320 [436,945,300,49,9],
%e A102320 [8122,17568,5425,784,81,11],
%e A102320 [197920,427770,130700,18081,1620,121,13],
%e A102320 [6007205,12979080,3947050,535864,45441,2904,169,15],...
%e A102320 Matrix square T^2 equals T excluding the main diagonal:
%e A102320 [1],
%e A102320 [4,9],
%e A102320 [33,72,25],
%e A102320 [436,945,300,49],
%e A102320 [8122,17568,5425,784,81],...
%o A102320 (PARI) {T(n,k)=local(A=Mat(1),B); for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=2*j-1,if(j==1,B[i,j]=(A^2)[i-1,1], B[i,j]=(A^2)[i-1,j]));));A=B);return(A[n+1,k+1])}
%Y A102320 Cf. A102086, A102321, A102322, A102323.
%K A102320 nonn,tabl
%O A102320 0,3
%A A102320 _Paul D. Hanna_, Jan 05 2005