%I #6 Jun 13 2017 23:21:04

%S 1,2,1,6,8,1,37,84,14,1,429,1296,252,20,1,7629,27850,5957,510,26,1,

%T 185776,784146,179270,16180,858,32,1,5817106,27630378,6641502,623115,

%U 34125,1296,38,1,224558216,1177691946,294524076,28470525,1599091,61952

%N Triangle, read by rows, equal to the matrix square of A113370. Also given by the product: P^2 = Q*(R^-2)*Q^3, using triangular matrices P=A113370, Q=A113381 and R=A113389.

%F Column k of A113370^2 = column 0 of A113381^(3*k+1).

%e Triangle A113370^2 begins:

%e 1;

%e 2,1;

%e 6,8,1;

%e 37,84,14,1;

%e 429,1296,252,20,1;

%e 7629,27850,5957,510,26,1;

%e 185776,784146,179270,16180,858,32,1;

%e 5817106,27630378,6641502,623115,34125,1296,38,1;

%e 224558216,1177691946,294524076,28470525,1599091,61952,1824,44,1;

%o (PARI) T(n,k)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(3*j-2))[i-j+1,1]));));A=B);(A^2)[n+1,k+1]

%Y Cf. A113370, A113381, A113389; A113375 (column 0), A113376 (column 1), A113377 (column 2); A113378 (P^3), A113387 (Q^3).

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Nov 14 2005