A154559 Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k))).

1, 2, 0, 3, 2, 0, 4, 6, 4, 0, 5, 12, 16, 9, 0, 6, 20, 40, 45, 21, 0, 7, 30, 80, 135, 126, 51, 0, 8, 42, 140, 315, 441, 357, 127, 0, 9, 56, 224, 630, 1176, 1428, 1016, 323, 0, 10, 72, 336, 1134, 2646, 4284, 4572, 2907, 835, 0

Offset: 1

Author

Gary W. Adamson, Jan 11 2009

Keywords

• nonn
• tabl

Comments

Row sums = the Catalan numbers, A000108, starting with offset 1:

(1, 2, 5, 14, 42,...).

Examples

			First few rows of the triangle =
1;
2, 0;
3, 2, 0;
4, 6, 4, 0;
5, 12, 16, 9, 0;
6, 20, 40, 45, 21, 0;
7, 30, 80, 135, 126, 51, 0;
8, 42, 140, 315, 441, 357, 127, 0;
9, 56, 224, 630, 1176, 1428, 1016, 323, 0;
10, 72, 336, 1134, 2646, 4284, 4572, 2907, 835, 0;
11, 90, 480, 1890, 5292, 10710, 15240, 14535, 8350, 2188;
12, 110, 660, 2970, 9702, 23562, 41910, 53295, 45925, 24068, 5798;
...
		

Crossrefs

Cf. A001006, A000108

Formula

Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k)))

Binomial transform of a bidiagonal matrix with (1,0,0,0,..,.) as the main

diagonal and A001006 as the subddiagonal starting (1, 2, 4, 9, 21, 51,...).