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%I #14 Feb 13 2022 23:16:21
%S 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,
%T 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,
%U 24,120,720,1067,456,93,10,1
%N Triangle read by rows, constructed from binomial transforms of prefixes of A000255 (see Comments for precise definition).
%C 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.
%C Replace each column of R by its binomial transform to get the matrix S.
%C The first few rows of S are
%C 1, 1, 1, 1, ...
%C 1, 2, 3, 4, ...
%C 1, 2, 6, 13, ...
%C 1, 2, 6, 24, ...
%C ...
%C Read S by antidiagonals to get the desired triangle, which begins
%C 1;
%C 1, 1;
%C 1, 2, 1;
%C 1, 2, 3, 1;
%C 1, 2, 6, 4, 1;
%C 1, 2, 6, 13, 5, 1;
%C 1, 2, 6, 24, 23, 6, 1;
%C 1, 2, 6, 24, 67, 36, 7, 1;
%C ...
%C Rows converge to sequence A000142 of factorial numbers.
%Y Cf. A000255, A010027.
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Feb 24 2006
%E Edited by _N. J. A. Sloane_, Aug 11 2019
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