A356115 - OEIS

%I #8 Aug 21 2022 14:09:48

%S 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,

%T 93,185,80,36,15,1,0,22,196,462,490,161,77,21,1,0,33,312,1120,1834,

%U 1050,336,148,28,1

%N 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.

%H Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook.

%e [ 1] [1]

%e [ 2] [0,  1]

%e [ 3] [0,  1,   1]

%e [ 4] [0,  3,   1,    1]

%e [ 5] [0,  4,   6,    3,    1]

%e [ 6] [0,  9,  20,    6,    6,    1]

%e [ 7] [0, 11,  45,   50,   15,   10,   1]

%e [ 8] [0, 19,  93,  185,   80,   36,  15,   1]

%e [ 9] [0, 22, 196,  462,  490,  161,  77,  21,  1]

%e [10] [0, 33, 312, 1120, 1834, 1050, 336, 148, 28, 1]

%o (SageMath) # uses function reduce_partition_triangle from A356265.

%o def A356115_row(n: int) -> list[int]:

%o     return reduce_partition_triangle(A356266_row, n + 1)[n - 1]

%o def A356115(n: int, k: int) -> int:

%o     return A356115_row(n)[k]

%o for n in range(1, 11):

%o     print([n], A356115_row(n))

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

%K nonn,tabl

%O 1,8

%A _Peter Luschny_, Aug 16 2022