cp's OEIS Frontend

A114158 Triangle, read by rows, equal to the matrix inverse of Q=A113381.

%I A114158 #5 Jun 13 2017 23:40:24
%S A114158 1,-2,1,4,-5,1,21,-5,-8,1,130,20,-32,-11,1,1106,840,-260,-77,-14,1,
%T A114158 10044,24865,-2584,-1089,-140,-17,1,-18366,823383,-12828,-21428,-2737,
%U A114158 -221,-20,1,-9321125,31847653,1160956,-523831,-73458,-5474,-320,-23,1
%N A114158 Triangle, read by rows, equal to the matrix inverse of Q=A113381.
%e A114158 Triangle Q^-1 begins:
%e A114158 1;
%e A114158 -2,1;
%e A114158 4,-5,1;
%e A114158 21,-5,-8,1;
%e A114158 130,20,-32,-11,1;
%e A114158 1106,840,-260,-77,-14,1;
%e A114158 10044,24865,-2584,-1089,-140,-17,1;
%e A114158 -18366,823383,-12828,-21428,-2737,-221,-20,1; ...
%e A114158 Triangle Q^-2 begins:
%e A114158 1;
%e A114158 -4,1;
%e A114158 18,-10,1;
%e A114158 20,30,-16,1;
%e A114158 -139,255,24,-22,1;
%e A114158 -3945,3085,544,0,-28,1;
%e A114158 -99849,51015,12444,671,-42,-34,1; ...
%o A114158 (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])); (Q^-1)[n+1,k+1]
%Y A114158 Cf. A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114151 (R^-2*Q^3=Q^-1*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), A114159 (R^-1).
%K A114158 sign,tabl
%O A114158 0,2
%A A114158 _Paul D. Hanna_, Nov 15 2005