A106194 Triangle read by rows, generated from binomial transforms of odd numbers.

1, 4, 1, 12, 5, 1, 32, 17, 6, 1, 80, 49, 23, 7, 1, 192, 129, 72, 30, 8, 1, 448, 321, 201, 102, 38, 9, 1, 1024, 769, 522, 303, 140, 47, 10, 1, 2304, 1793, 1291, 825, 443, 187, 57, 11, 1, 5120, 4097, 3084, 2116, 1268, 630, 244, 68, 12, 1

Offset: 0

Author

Gary W. Adamson, Apr 24 2005

Keywords

• nonn
• tabl

Comments

Appending the binomial transform of the natural numbers, (A001792: 1, 3, 8, 20, 48...) to A106194 as a leftmost column creates triangle A055249.

Placing zeros into the offset spaces, column 1: 0, 1, 5, 17, 49...; is the binomial transform of 0, 1, 3, 5...; and alternatively the binomial transform of 0, 0, 1, 2, 3...

n-th column is the binomial transform of 1, 3, 5...prefaced by n zeros. n-th column is alternatively the binomial transform of 1, 2, 3...prefaced by (n+1) zeros. The triangle of A106194 is identical to the binomial transform (of natural numbers, prefaced with zeros) triangle: A055249, deleting the leftmost column.

Examples

			First few rows of the triangle are:
1;
4, 1;
12, 5, 1;
32, 17, 6, 1;
80, 49, 23, 7, 1;
192, 129, 72, 30, 8, 1;
448, 321, 201, 102, 38, 9, 1;
...
		

Crossrefs

Cf. A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055249.