

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

Row sums = A000995 such that row 1 = A000995(3) = 1.
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

Table of n, a(n) for n=1..54.


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 are:
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 are:
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

Cf. A000995, A008277.
Sequence in context: A202979 A306326 A156006 * A062715 A100631 A154867
Adjacent sequences: A137851 A137852 A137853 * A137855 A137856 A137857


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 15 2008


STATUS

approved



