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

1, -2, 1, 4, -5, 1, 21, -5, -8, 1, 130, 20, -32, -11, 1, 1106, 840, -260, -77, -14, 1, 10044, 24865, -2584, -1089, -140, -17, 1, -18366, 823383, -12828, -21428, -2737, -221, -20, 1, -9321125, 31847653, 1160956, -523831, -73458, -5474, -320, -23, 1

Offset: 0

Author

Paul D. Hanna, Nov 15 2005

Keywords

• sign
• tabl

Examples

			Triangle Q^-1 begins:
1;
-2,1;
4,-5,1;
21,-5,-8,1;
130,20,-32,-11,1;
1106,840,-260,-77,-14,1;
10044,24865,-2584,-1089,-140,-17,1;
-18366,823383,-12828,-21428,-2737,-221,-20,1; ...
Triangle Q^-2 begins:
1;
-4,1;
18,-10,1;
20,30,-16,1;
-139,255,24,-22,1;
-3945,3085,544,0,-28,1;
-99849,51015,12444,671,-42,-34,1; ...
		

Crossrefs

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).

Programs

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]