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A113368 Triangle, read by rows, given by the product Q^-1*P^2, where the triangular matrices involved are P = A113340 and Q = A113350.

%I A113368 #5 Jun 13 2017 23:21:16
%S A113368 1,0,1,0,2,1,0,5,4,1,0,19,22,6,1,0,113,166,51,8,1,0,966,1671,561,92,
%T A113368 10,1,0,10958,21510,7726,1324,145,12,1,0,156700,341463,129406,23010,
%U A113368 2575,210,14,1,0,2727794,6496923,2572892,471724,53935,4434,287,16,1
%N A113368 Triangle, read by rows, given by the product Q^-1*P^2, where the triangular matrices involved are P = A113340 and Q = A113350.
%C A113368 Matrix product Q^-1*P^2 = SHIFT_DOWN_RIGHT(Q). Compare to the matrix product Q^2*P^-1 = SHIFT_LEFT_UP(P), as given by triangle A113369.
%e A113368 The product Q^-1*P^2 forms a triangle that begins:
%e A113368 1;
%e A113368 0,1;
%e A113368 0,2,1;
%e A113368 0,5,4,1;
%e A113368 0,19,22,6,1;
%e A113368 0,113,166,51,8,1;
%e A113368 0,966,1671,561,92,10,1;
%e A113368 0,10958,21510,7726,1324,145,12,1;
%e A113368 0,156700,341463,129406,23010,2575,210,14,1;
%e A113368 0,2727794,6496923,2572892,471724,53935,4434,287,16,1; ...
%e A113368 Compare Q^-1*P^2 to Q (A113350) which begins:
%e A113368 1;
%e A113368 2,1;
%e A113368 5,4,1;
%e A113368 19,22,6,1;
%e A113368 113,166,51,8,1;
%e A113368 966,1671,561,92,10,1;
%e A113368 10958,21510,7726,1324,145,12,1; ...
%o A113368 (PARI) T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=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^(2*j-1))[i-j+1,1]));));A=B);(A^(2*k))[n-k+1,1]
%Y A113368 Cf. A113340, A113350, A113369 (Q^2*P^-1).
%K A113368 nonn,tabl
%O A113368 0,5
%A A113368 _Paul D. Hanna_, Nov 12 2005