A140733 Triangle read by rows, X^n * [1,0,0,0,...]; where X = a tridiagonal matrix with (1,1,1,...) in the main and subdiagonals and (1,2,3,...) in the subsubdiagonal.

1, 1, 1, 1, 1, 2, 3, 3, 3, 1, 3, 6, 10, 15, 15, 15, 1, 4, 10, 22, 43, 70, 105, 105, 105, 1, 5, 15, 40, 95, 201, 390, 630, 945, 945, 945, 1, 6, 21, 65, 180, 456, 1066, 2226, 4305, 6930, 10395, 10395, 10395, 1, 7, 28, 98, 308, 896, 2422, 6028, 13993, 29043, 56070, 90090

Offset: 1

Author

Gary W. Adamson & Roger L. Bagula, May 25 2008

Keywords

• nonn
• tabl

Comments

Rightmost terms of each row form A001147: (1, 1, 3, 15, 105, 945,...).

Examples

			First few rows of the triangle are:
1;
1, 1, 1;
1, 2, 3, 3, 3;
1, 3, 6, 10, 15, 15, 15;
1, 4, 10, 22, 43, 70, 105, 105, 105;
1, 5, 15, 40, 95, 201, 390, 630, 945, 945, 945;
1, 6, 21, 65, 180, 456, 1066, 2226, 4305, 6930, 10395, 10395, 10395;
...
		

Crossrefs

Cf. A140734, A140735, A001147.