A113368 Triangle, read by rows, given by the product Q^-1*P^2, where the triangular matrices involved are P = A113340 and Q = A113350.

1, 0, 1, 0, 2, 1, 0, 5, 4, 1, 0, 19, 22, 6, 1, 0, 113, 166, 51, 8, 1, 0, 966, 1671, 561, 92, 10, 1, 0, 10958, 21510, 7726, 1324, 145, 12, 1, 0, 156700, 341463, 129406, 23010, 2575, 210, 14, 1, 0, 2727794, 6496923, 2572892, 471724, 53935, 4434, 287, 16, 1

Offset: 0

Author

Paul D. Hanna, Nov 12 2005

Keywords

• nonn
• tabl

Comments

Matrix product Q^-1*P^2 = SHIFT_DOWN_RIGHT(Q). Compare to the matrix product Q^2*P^-1 = SHIFT_LEFT_UP(P), as given by triangle A113369.

Examples

			The product Q^-1*P^2 forms a triangle that begins:
1;
0,1;
0,2,1;
0,5,4,1;
0,19,22,6,1;
0,113,166,51,8,1;
0,966,1671,561,92,10,1;
0,10958,21510,7726,1324,145,12,1;
0,156700,341463,129406,23010,2575,210,14,1;
0,2727794,6496923,2572892,471724,53935,4434,287,16,1; ...
Compare Q^-1*P^2 to Q (A113350) which begins:
1;
2,1;
5,4,1;
19,22,6,1;
113,166,51,8,1;
966,1671,561,92,10,1;
10958,21510,7726,1324,145,12,1; ...
		

Crossrefs

Cf. A113340, A113350, A113369 (Q^2*P^-1).

Programs

PARI

T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,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^(2*k))[n-k+1,1]