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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
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
Sequence in context: A202979 A306326 A156006 * A062715 A100631 A154867
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 15 2008
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)