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A114151 Triangle, read by rows, given by the product R^-2*Q^3 = Q^-1*P^2 using triangular matrices P=A113370, Q=A113381, R=A113389.

%I A114151 #5 Jun 13 2017 23:39:50
%S A114151 1,0,1,0,3,1,0,15,6,1,0,136,66,9,1,0,1998,1091,153,12,1,0,41973,24891,
%T A114151 3621,276,15,1,0,1166263,737061,110637,8482,435,18,1,0,40747561,
%U A114151 27110418,4176549,323874,16430,630,21,1
%N A114151 Triangle, read by rows, given by the product R^-2*Q^3 = Q^-1*P^2 using triangular matrices P=A113370, Q=A113381, R=A113389.
%C A114151 Complementary to A114150, which gives R^2*Q^-1 = Q^3*P^-2.
%e A114151 Triangle R^-2*Q^3 = Q^-1*P^2 begins:
%e A114151 1;
%e A114151 0,1;
%e A114151 0,3,1;
%e A114151 0,15,6,1;
%e A114151 0,136,66,9,1;
%e A114151 0,1998,1091,153,12,1;
%e A114151 0,41973,24891,3621,276,15,1; ...
%e A114151 Compare to R (A113389):
%e A114151 1;
%e A114151 3,1;
%e A114151 15,6,1;
%e A114151 136,66,9,1;
%e A114151 1998,1091,153,12,1;
%e A114151 41973,24891,3621,276,15,1; ...
%e A114151 Thus R^-2*Q^3 = Q^-1*P^2 equals R shift right one column.
%o A114151 (PARI) T(n,k)=local(P,Q,R,W);P=Mat(1);for(m=2,n+1,W=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,W[i,j]=1,if(j==1, W[i,1]=1,W[i,j]=(P^(3*j-2))[i-j+1,1]));));P=W); Q=matrix(#P,#P,r,c,if(r>=c,(P^(3*c-1))[r-c+1,1])); R=matrix(#P,#P,r,c,if(r>=c,(P^(3*c))[r-c+1,1])); (Q^-1*P^2)[n+1,k+1]
%Y A114151 Cf. A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114152 (R^3*P^-1), A114153 (R^-1*P^3), A114154 (R^3*Q^-2), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1), A114159 (R^-1).
%K A114151 nonn,tabl
%O A114151 0,5
%A A114151 _Paul D. Hanna_, Nov 15 2005