A130461 Triangle, antidiagonals of an array generated from A130460.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 6, 4, 1, 1, 1, 2, 6, 12, 5, 1, 1, 1, 2, 6, 24, 20, 6, 1, 1, 1, 2, 6, 24, 60, 30, 7, 1, 1, 1, 2, 6, 24, 120, 120, 42, 8, 1, 1, 1, 2, 6, 24, 120, 360, 210, 56, 9, 1, 1, 1, 2, 6, 24, 120, 720, 840, 336, 72, 10, 1, 1, 1, 2, 6, 24, 120, 720, 2520

Offset: 0

Author

Gary W. Adamson, May 28 2007

Keywords

• nonn
• tabl

Comments

Rows tend to the factorials: (1, 1, 2, 6, 24, ...). Row sums = A130476: (1, 2, 3, 5, 8, 15, 28, 61, 132, ...).

Examples

			The array =
  1, 1, 1, 1,  1,   1, ...
  1, 1, 2, 3,  4,   5, ...
  1, 1, 2, 6, 12,  20, ...
  1, 1, 2, 6, 24,  60, ...
  1, 1, 2, 6, 24, 120, ...
  1, 1, 2, 6, 24, 120, ...
  ...
First few rows of the triangle:
  1;
  1, 1;
  1, 1, 1;
  1, 1, 2, 1;
  1, 1, 2, 3,  1;
  1, 1, 2, 6,  4,  1;
  1, 1, 2, 6, 12,  5,  1;
  1, 1, 2, 6, 24, 20,  6, 1;
  1, 1, 2, 6, 24, 60, 30, 7, 1;
  ...
		

Crossrefs

Cf. A130460, A130476, A130477, A130478.

Formula

Let A130460 = M, an infinite lower triangular matrix and V = [1, 1, 1, ...], the first row of an array. Perform M * V = second row, ...; (n+1)-th row = M * n-th row. The triangle = antidiagonals of the array.

Extensions

a(23) and a(38) corrected by Gionata Neri, Jun 22 2016