A154109 Convolution triangle by rows, A004736 * (A154108 * 0^(n-k)); row sums = Bell numbers.

1, 2, 0, 3, 0, 2, 4, 0, 4, 7, 5, 0, 6, 14, 27, 6, 0, 8, 21, 54, 114, 7, 0, 10, 28, 81, 228, 523, 8, 0, 12, 35, 108, 342, 1046, 2589, 9, 0, 14, 42, 135, 456, 1569, 5178, 13744, 10, 0, 16, 49, 162, 570, 2092, 7767, 27488, 77821

Offset: 1

Author

Gary W. Adamson, Jan 04 2009

Keywords

• nonn
• tabl

Comments

Row sums = Bell numbers, A000110 starting (1, 2, 5, 15, 52, 203, 877,...).

Examples

			First few rows of the triangle =
1;
2, 0;
3, 0, 2;
4, 0, 4, 7;
5, 0, 6, 14, 27;
6, 0, 8, 21, 54, 114;
7, 0, 10, 28, 81, 228, 523;
8, 0, 12, 35, 108, 342, 1046, 2589;
9, 0, 14, 42, 135, 456, 1569, 5178, 13744;
10, 0, 16, 49, 162, 570, 2092, 7767, 27488, 77821;
...
Row 5 = (5, 0, 6, 14, 27), sum = A000110(5) = 52 = termwise products of
(5, 4, 3, 2, 1) and (1, 0, 2, 7, 27).
		

Crossrefs

Cf. A154108, A000110.

Formula

A004736 * (A154108 * 0^(n-k)); where A004736 = an infinite lower triangular

matrix with (1,2,3,...) in every column and (A154108 * 0^(n-k)) = a matrix

with A154108 (1, 0, 2, 7, 27, 114, 523, 2589...) as the main diagonal

and the rest zeros.