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

0,2

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.

Links

Table of n, a(n) for n=0..44.

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

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

Sequence in context: A226167 A185105 A122844 * A249253 A201638 A127894

Adjacent sequences: A113366 A113367 A113368 * A113370 A113371 A113372

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 12 2005

Status

approved