The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)