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A113392 Triangle, read by rows, equal to the matrix square of triangle A113389. Also given by the matrix product: R^2 = Q^3*(P^-2)*Q, using triangular matrices P=A113370, Q=A113381 and R=A113389.

%I A113392 #6 Jun 13 2017 23:30:42
%S A113392 1,6,1,48,12,1,605,186,18,1,11196,3892,414,24,1,280440,106089,12021,
%T A113392 732,30,1,8981460,3620379,429345,27152,1140,36,1,353283128,149740555,
%U A113392 18386361,1196910,51445,1638,42,1,16567072675,7316974618,923656512
%N A113392 Triangle, read by rows, equal to the matrix square of triangle A113389. Also given by the matrix product: R^2 = Q^3*(P^-2)*Q, using triangular matrices P=A113370, Q=A113381 and R=A113389.
%e A113392 Triangle A113389^2 begins:
%e A113392 1;
%e A113392 6,1;
%e A113392 48,12,1;
%e A113392 605,186,18,1;
%e A113392 11196,3892,414,24,1;
%e A113392 280440,106089,12021,732,30,1;
%e A113392 8981460,3620379,429345,27152,1140,36,1;
%e A113392 353283128,149740555,18386361,1196910,51445,1638,42,1;
%e A113392 16567072675,7316974618,923656512,61515702,2696010,87060,2226,48,1;
%o A113392 (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); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c))[r-c+1,1]))^2)[n+1,k+1]
%Y A113392 Cf. A113389, A113388 (column 0), A113393 (column 1).
%K A113392 nonn,tabl
%O A113392 0,2
%A A113392 _Paul D. Hanna_, Nov 14 2005