A165194 Triangle of 2^n terms by rows, left half of (n+1)-th row = row n; right half = "reverse and increment" row n; using terms in A000110.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 5, 2, 1, 1, 1, 2, 1, 2, 5, 2, 1, 1, 2, 5, 15, 5, 2, 5, 2, 1

Offset: 1

Author

Gary W. Adamson, Sep 06 2009

Keywords

• nonn
• tabf

Comments

Row sums = A000110, the Bell sequence starting with offset 1; (1, 2, 5, 15,...).

Rows tend to A165195.

Examples

			First few rows of the triangle =
1;
1, 1;
1, 1, 2, 1;
1, 1, 2, 1, 2, 5, 2, 1;
1, 1, 2, 1, 2, 5, 2, 1, 2, 5, 15, 5, 2, 5, 2, 1;
...
For example: row 4, left half = (1, 1, 2, 1); right half = (1, 2, 1, 1)
replaced with the next higher Bell numbers: (2, 5, 2, 1). Appending the two \kQ halves, we obtain row 4: (1, 1, 2, 1, 2, 5, 2, 1), sum = 15 = A000110(4).
		

Crossrefs

A000110, A165195, A165196

Formula

Given the Bell sequence, A000110: (1, 1, 2, 5, 15,...); row 1 = 1, row 2 =

(1, 1);...where left half of row (n+1) = row n. Right half of row (n+1)

= reversal of row n, replacing terms with the next Bell number.