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A154559 Triangle read by rows, A007318 * (A129186 * (A001006 * 0^(n-k)) 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..55.

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,...).

EXAMPLE

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

Sequence in context: A187637 A141432 A115241 * A269133 A143324 A287416

Adjacent sequences:  A154556 A154557 A154558 * A154560 A154561 A154562

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jan 11 2009

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.