A114159 Triangle, read by rows, equal to the matrix inverse of R=A113389.

1, -3, 1, 3, -6, 1, 35, -12, -9, 1, 396, -29, -45, -12, 1, 6237, 582, -462, -96, -15, 1, 131613, 30684, -6408, -1534, -165, -18, 1, 3518993, 1300810, -96705, -34020, -3515, -252, -21, 1, 114244366, 59124226, -764835, -944334, -102180, -6675, -357, -24, 1

Offset: 0

Author

Paul D. Hanna, Nov 15 2005

Keywords

• sign
• tabl

Examples

			Triangle R^-1 begins:
  1;
  -3,1;
  3,-6,1;
  35,-12,-9,1;
  396,-29,-45,-12,1;
  6237,582,-462,-96,-15,1;
  131613,30684,-6408,-1534,-165,-18,1;
  3518993,1300810,-96705,-34020,-3515,-252,-21,1;
  ...
Triangle R^-2 begins:
  1;
  -6,1;
  24,-12,1;
  79,30,-18,1;
  324,356,18,-24,1;
  42,5523,615,-12,-30,1;
  -79346,112533,16731,640,-60,-36,1;
  ...
		

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), A114158 (Q^-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); R=matrix(#P,#P,r,c,if(r>=c,(P^(3*c))[r-c+1,1])); (R^-1)[n+1,k+1]}