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

1,6

Comments

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

Links

Table of n, a(n) for n=1..61.

Example

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.

Sequence in context: A082239 A207814 A062745 * A143605 A098418 A364367

Adjacent sequences: A140730 A140731 A140732 * A140734 A140735 A140736

Keyword

nonn,tabl

Author

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

Status

approved