A116855 Triangle read by rows, constructed from binomial transforms of prefixes of A000255 (see Comments for precise definition).

1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 6, 4, 1, 1, 2, 6, 13, 5, 1, 1, 2, 6, 24, 23, 6, 1, 1, 2, 6, 24, 67, 36, 7, 1, 1, 2, 6, 24, 120, 146, 52, 8, 1, 1, 2, 6, 24, 120, 411, 272, 71, 9, 1, 1, 2, 6, 24, 120, 720, 1067, 456, 93, 10, 1

Offset: 1

Author

Gary W. Adamson, Feb 24 2006

Keywords

• nonn
• tabl

Comments

Form a matrix R whose columns are [1,0,0,0,...], [1,1,0,0,0,...], [1,1,3,0,0,0,...], [1,1,3,11,0,0,0,...], [1,1,3,11,53,0,0,0,...], ..., formed from the prefixes of A000255 each padded with infinitely many zeros.

Replace each column of R by its binomial transform to get the matrix S.

Rows converge to sequence A000142 of factorial numbers.

Examples

			The first few rows of S are
  1, 1, 1,  1, ...
  1, 2, 3,  4, ...
  1, 2, 6, 13, ...
  1, 2, 6, 24, ...
  ...
Read S by antidiagonals to get the desired triangle, which begins
  1;
  1, 1;
  1, 2, 1;
  1, 2, 3,  1;
  1, 2, 6,  4,  1;
  1, 2, 6, 13,  5,  1;
  1, 2, 6, 24, 23,  6, 1;
  1, 2, 6, 24, 67, 36, 7, 1;
  ...
		

Crossrefs

Cf. A000255, A010027.

Extensions

Edited by N. J. A. Sloane, Aug 11 2019