A116855 - OEIS

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

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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.

Rows converge to sequence A000142 of factorial numbers.

LINKS

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

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