OFFSET
0,2
COMMENTS
Matrix product Q^2*P^-1 = SHIFT_LEFT_UP(P). Compare to the matrix product Q^-1*P^2 = SHIFT_DOWN_RIGHT(Q), as given by triangle A113368.
EXAMPLE
The product Q^2*P^-1 forms a triangle that begins:
1;
3,1;
12,5,1;
69,35,7,1;
560,325,70,9,1;
6059,3880,889,117,11,1;
83215,57560,13853,1881,176,13,1;
1399161,1030751,258146,36051,3421,247,15,1;
28020221,21763632,5633264,805875,77726,5629,330,17,1; ...
Compare Q^2*P^-1 to P (A113340) which begins:
1;
1,1;
1,3,1;
1,12,5,1;
1,69,35,7,1;
1,560,325,70,9,1;
1,6059,3880,889,117,11,1;
1,83215,57560,13853,1881,176,13,1; ...
PROG
(PARI) T(n, k)=local(A, B); A=matrix(1, 1); A[1, 1]=1; for(m=2, n+2, B=matrix(m, m); for(i=1, m, for(j=1, i, if(i<3 || j==i || j>m-1, B[i, j]=1, if(j==1, B[i, 1]=1, B[i, j]=(A^(2*j-1))[i-j+1, 1])); )); A=B); A[n+2, k+2]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Nov 12 2005
STATUS
approved