1,2

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

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

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,...).

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;

...

Cf. A001006, A000108

Sequence in context: A127479 A141432 A115241 this_sequence A143324 A097418 A154752

Adjacent sequences: A154556 A154557 A154558 this_sequence A154560 A154561 A154562

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 11 2009