A113369 Triangle, read by rows, given by the product Q^2*P^-1, where the triangular matrices involved are P = A113340 and Q = A113350.

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

Offset: 0

Author

Paul D. Hanna, Nov 12 2005

Keywords

• nonn
• tabl

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.

Examples

			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; ...
		

Crossrefs

Cf. A113340, A113350, A113368 (Q^-1*P^2).

Programs

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]