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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 (list; table; graph; refs; listen; history; text; internal format)
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 1-23 and 3-12, 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

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Last modified October 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)