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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)