A114158 - OEIS

%I #5 Jun 13 2017 23:40:24

%S 1,-2,1,4,-5,1,21,-5,-8,1,130,20,-32,-11,1,1106,840,-260,-77,-14,1,

%T 10044,24865,-2584,-1089,-140,-17,1,-18366,823383,-12828,-21428,-2737,

%U -221,-20,1,-9321125,31847653,1160956,-523831,-73458,-5474,-320,-23,1

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

%e Triangle Q^-1 begins:

%e 1;

%e -2,1;

%e 4,-5,1;

%e 21,-5,-8,1;

%e 130,20,-32,-11,1;

%e 1106,840,-260,-77,-14,1;

%e 10044,24865,-2584,-1089,-140,-17,1;

%e -18366,823383,-12828,-21428,-2737,-221,-20,1; ...

%e Triangle Q^-2 begins:

%e 1;

%e -4,1;

%e 18,-10,1;

%e 20,30,-16,1;

%e -139,255,24,-22,1;

%e -3945,3085,544,0,-28,1;

%e -99849,51015,12444,671,-42,-34,1; ...

%o (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 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 sign,tabl

%O 0,2

%A _Paul D. Hanna_, Nov 15 2005