A114156 Triangle, read by rows, equal to the matrix inverse of P=A113370.

1, -1, 1, 3, -4, 1, 6, 0, -7, 1, -8, 38, -21, -10, 1, -501, 692, -119, -60, -13, 1, -13623, 14910, -420, -735, -117, -16, 1, -409953, 401802, 22911, -12470, -2080, -192, -19, 1, -14544683, 13278520, 1577527, -255570, -51064, -4424, -285, -22, 1

Offset: 0

Author

Paul D. Hanna, Nov 15 2005

Keywords

• sign
• tabl

Examples

			Triangle P^-1 begins:
1;
-1,1;
3,-4,1;
6,0,-7,1;
-8,38,-21,-10,1;
-501,692,-119,-60,-13,1;
-13623,14910,-420,-735,-117,-16,1;
-409953,401802,22911,-12470,-2080,-192,-19,1; ...
Triangle P^-2 begins:
1;
-2,1;
10,-8,1;
-9,28,-14,1;
-177,160,28,-20,1;
-2307,1366,455,10,-26,1;
-38874,15982,8666,660,-26,-32,1; ...
		

Crossrefs

Cf. A114157 (column 0), 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); A114158 (Q^-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); (P^-1)[n+1,k+1]