login
A356263
Triangle read by rows. The reduced triangle of the partition triangle of irreducible permutations (A356262). T(n, k) for n >= 1 and 0 <= k < n.
3
1, 0, 1, 0, 2, 1, 0, 3, 9, 1, 0, 5, 41, 24, 1, 0, 8, 150, 247, 55, 1, 0, 14, 494, 1746, 1074, 118, 1, 0, 24, 1537, 10126, 13110, 4050, 245, 1, 0, 43, 4642, 52129, 122521, 79396, 14111, 500, 1, 0, 77, 13745, 248494, 967644, 1126049, 425471, 46833, 1011, 1
OFFSET
1,5
COMMENTS
The triangle can be seen as Euler's triangle A008292 restricted to irreducible permutations.
See the comments in A356116 for the definition of the terms 'partition triangle' and 'reduced partition triangle'. The reduction procedure is formalized in the Sage program in A356116.
LINKS
Peter Luschny, Permutations with Lehmer, a SageMath Jupyter Notebook.
EXAMPLE
[1] [1]
[2] [0, 1]
[3] [0, 2, 1]
[4] [0, 3, 9, 1]
[5] [0, 5, 41, 24, 1]
[6] [0, 8, 150, 247, 55, 1]
[7] [0, 14, 494, 1746, 1074, 118, 1]
[8] [0, 24, 1537, 10126, 13110, 4050, 245, 1]
[9] [0, 43, 4642, 52129, 122521, 79396, 14111, 500, 1]
[10][0, 77, 13745, 248494, 967644, 1126049, 425471, 46833, 1011, 1]
.
The 5 irreducible permutations counted with T(5, 2) are 23451, 51234, 31524, 34512, and 45123.
PROG
(SageMath) # Uses function 'reduce_partition_triangle' from A356116.
reduce_partition_triangle(A356262_row, 8)
CROSSREFS
Cf. A356262 (partition triangle), A007059 (column 2), A003319 (row sums), A356114 (subdiagonal).
Sequence in context: A278882 A153007 A090683 * A320825 A161552 A366592
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 01 2022
STATUS
approved