A356115 Triangle read by rows. The reduced triangle of the partition triangle of reducible permutations with weakly decreasing Lehmer code (A356266). T(n, k) for n >= 1 and 0 <= k < n.

1, 0, 1, 0, 1, 1, 0, 3, 1, 1, 0, 4, 6, 3, 1, 0, 9, 20, 6, 6, 1, 0, 11, 45, 50, 15, 10, 1, 0, 19, 93, 185, 80, 36, 15, 1, 0, 22, 196, 462, 490, 161, 77, 21, 1, 0, 33, 312, 1120, 1834, 1050, 336, 148, 28, 1

Offset: 1

Author

Peter Luschny, Aug 16 2022

Keywords

• nonn
• tabl

Examples

			[ 1] [1]
[ 2] [0,  1]
[ 3] [0,  1,   1]
[ 4] [0,  3,   1,    1]
[ 5] [0,  4,   6,    3,    1]
[ 6] [0,  9,  20,    6,    6,    1]
[ 7] [0, 11,  45,   50,   15,   10,   1]
[ 8] [0, 19,  93,  185,   80,   36,  15,   1]
[ 9] [0, 22, 196,  462,  490,  161,  77,  21,  1]
[10] [0, 33, 312, 1120, 1834, 1050, 336, 148, 28, 1]
		

Links

• Peter Luschny, Permutations with Lehmer, a SageMath Jupyter Notebook.

Crossrefs

Cf. A356266 (partition version), A356265, A120588 (row sums).

Programs

SageMath

# uses function reduce_partition_triangle from A356265.
def A356115_row(n: int) -> list[int]:
    return reduce_partition_triangle(A356266_row, n + 1)[n - 1]
def A356115(n: int, k: int) -> int:
    return A356115_row(n)[k]
for n in range(1, 11):
    print([n], A356115_row(n))