

A137854


Triangle generated from an array: A008277 * A008277(transform).


1



1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 11, 8, 1, 1, 16, 28, 28, 16, 1, 1, 32, 71, 87, 71, 32, 1, 1, 64, 184, 266, 266, 184, 64, 1, 1, 128, 491, 823, 952, 823, 491, 128, 1, 1, 256, 1348, 2598, 3381, 381, 2598, 1348, 2561
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OFFSET

1,5


COMMENTS

This array is the product of the lower triangular Stirling matrix and its transpose, which explains why the array is symmetric.  David Callan, Dec 02 2011
In the triangle, T(n,k) is the number of permutations of [n+1] that avoid both dashed patterns 123 and 312, start with an ascent, and have first entry k. For example, T(4,2)=4 counts 23154, 24153, 24315, 25431.  David Callan, Dec 02 2011


LINKS



FORMULA

Triangle read by rows = antidiagonals of an array formed by A008277 * A008277(transform), where A008277 = the Stirling number of the second kind triangle.


EXAMPLE

First few rows of the array:
1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, ...
1, 4, 11, 28, 71, 184, ...
1, 8, 28, 87, 266, 823, ...
1, 16, 71, 266, 952, 3381, ...
...
First few rows of the triangle:
1;
1, 1;
1, 2, 1;
1, 4, 4, 1;
1, 8, 11, 8, 1;
1, 16, 28, 28, 16, 1;
1, 32, 71, 87, 71, 32, 1;
1, 64, 184, 266, 266, 184, 64, 1;
1, 128, 491, 823, 952, 823, 491, 128, 1;
...


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



