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A113369 Triangle, read by rows, given by the product Q^2*P^-1, where the triangular matrices involved are P = A113340 and Q = A113350.

%I A113369 #5 Jun 13 2017 23:21:13
%S A113369 1,3,1,12,5,1,69,35,7,1,560,325,70,9,1,6059,3880,889,117,11,1,83215,
%T A113369 57560,13853,1881,176,13,1,1399161,1030751,258146,36051,3421,247,15,1,
%U A113369 28020221,21763632,5633264,805875,77726,5629,330,17,1
%N A113369 Triangle, read by rows, given by the product Q^2*P^-1, where the triangular matrices involved are P = A113340 and Q = A113350.
%C A113369 Matrix product Q^2*P^-1 = SHIFT_LEFT_UP(P). Compare to the matrix product Q^-1*P^2 = SHIFT_DOWN_RIGHT(Q), as given by triangle A113368.
%e A113369 The product Q^2*P^-1 forms a triangle that begins:
%e A113369 1;
%e A113369 3,1;
%e A113369 12,5,1;
%e A113369 69,35,7,1;
%e A113369 560,325,70,9,1;
%e A113369 6059,3880,889,117,11,1;
%e A113369 83215,57560,13853,1881,176,13,1;
%e A113369 1399161,1030751,258146,36051,3421,247,15,1;
%e A113369 28020221,21763632,5633264,805875,77726,5629,330,17,1; ...
%e A113369 Compare Q^2*P^-1 to P (A113340) which begins:
%e A113369 1;
%e A113369 1,1;
%e A113369 1,3,1;
%e A113369 1,12,5,1;
%e A113369 1,69,35,7,1;
%e A113369 1,560,325,70,9,1;
%e A113369 1,6059,3880,889,117,11,1;
%e A113369 1,83215,57560,13853,1881,176,13,1; ...
%o A113369 (PARI) T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+2,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^(2*j-1))[i-j+1,1]));));A=B);A[n+2,k+2]
%Y A113369 Cf. A113340, A113350, A113368 (Q^-1*P^2).
%K A113369 nonn,tabl
%O A113369 0,2
%A A113369 _Paul D. Hanna_, Nov 12 2005