login
A116855
Triangle read by rows, constructed from binomial transforms of prefixes of A000255 (see Comments for precise definition).
0
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
1,5
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.
EXAMPLE
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
Sequence in context: A179749 A103462 A225641 * A173265 A157744 A335545
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 24 2006
EXTENSIONS
Edited by N. J. A. Sloane, Aug 11 2019
STATUS
approved