A160708 Convolution triangle by rows, row sums = the Robbins sequence, A005130 starting with offset 1.

1, 1, 1, 3, 1, 3, 18, 3, 3, 18, 192, 18, 9, 18, 192, 3472, 192, 54, 54, 192, 3472, 104964, 3472, 576, 324, 576, 3472, 104964, 5606272, 104964, 10416, 3456, 3456, 10416, 104964, 5306272

Offset: 1

Author

Gary W. Adamson, May 24 2009

Keywords

• nonn
• tabl
• less

Comments

The terms are not integral in general, see A160707. - Joerg Arndt, Jan 02 2019

Row sums = the Robbins sequence A005130, starting with offset 1: (1, 2, 7, 42, 429,...).

Right and left borders = A160707, the convolution square root of A005130.

Examples

			First few rows of the triangle =
1;
1, 1;
3, 1, 3;
18, 3, 3, 18;
192, 18, 9, 18, 192;
3472, 192, 54, 54, 192, 3472;
104964, 3472, 576, 324, 576, 3472, 104964;
5606272, 104964, 10416, 3456, 3456, 10416, 104964, 5306272;
...
Example: row 5 = (192, 18, 9, 18, 192) = (192, 18, 3, 1, 1) * (1, 1, 3, 18, 192); where A005130(5) = 429 = (192 + 18 + 9 + 18 + 192).
		

Crossrefs

Cf. A005130, A160707

Formula

Let M = an infinite lower triangular Toeplitz matrix with A160707 in every column: (1, 1, 3, 18, 192, 5472,...); where A160707 = the convolution square root of the Robbins sequence: (1, 2, 7, 42, 429, 7436,...). Let Q = an infinite lower triangular matrix with (1, 1, 3, 18, 192,...) as the main diagonal and the rest zeros. Triangle A160708 = M * Q.