

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
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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.
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;
...
Rows converge to sequence A000142 of factorial numbers.


LINKS

Table of n, a(n) for n=1..66.


CROSSREFS

Cf. A000255, A010027.
Sequence in context: A179749 A103462 A225641 * A173265 A157744 A030111
Adjacent sequences: A116852 A116853 A116854 * A116856 A116857 A116858


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 24 2006


EXTENSIONS

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


STATUS

approved



