A131251 A000012 * A052509.

1, 2, 1, 3, 3, 1, 4, 6, 3, 1, 5, 10, 7, 3, 1, 6, 15, 14, 7, 3, 1, 7, 21, 25, 15, 7, 3, 1, 8, 28, 41, 30, 15, 7, 3, 1, 9, 36, 63, 56, 31, 15, 7, 3, 1, 10, 45, 92, 98, 62, 31, 15, 7, 3, 1

Offset: 0

Author

Gary W. Adamson, Jun 23 2007

Keywords

• nonn
• tabl

Comments

Row sums = A001924: (1, 3, 7, 14, 26, 46, 79, ...). A131252 = A052509 * A000012.

From Clark Kimberling, Feb 07 2011: (Start)

When formatted as a rectangle R with northwest corner

1, 2, 3, 4, 5, 6, ...

1, 3, 6, 10, 15, 21, ...

1, 3, 7, 14, 25, 41, ...

1, 3, 7, 15, 30, 56, ...

1, 3, 7, 15, 31, 62, ...

...

the following properties hold:

R is the accumulation array of the transpose of A052553 (a version of Pascal's triangle); see A144112 for the definition of accumulation array.

row 1: A000027

row 2: A000217

row 3: A004006

row 4: A055795

row 5: A057703

row 6: A115567

limiting row: A000225

antidiagonal sums: A001924.

(End)

Examples

			First few rows of the triangle:
  1;
  2,  1;
  3,  3,  1;
  4,  6,  3,  1;
  5, 10,  7,  3,  1;
  6, 15, 14,  7,  3,  1;
  7, 21, 25, 15,  7,  3,  1;
  ...
		

Crossrefs

Cf. A052509, A000012, A001924, A131252.

Formula

A000012 * A052509 as infinite lower triangular matrices.