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.

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

Table of n, a(n) for n=1..55.

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).

Cf. A008292, A356116.

Sequence in context: A278882 A153007 A090683 * A320825 A161552 A366592

Adjacent sequences: A356260 A356261 A356262 * A356264 A356265 A356266

Keyword

nonn,tabl

Author

Peter Luschny, Aug 01 2022

Status

approved