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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.

%I A356115 #8 Aug 21 2022 14:09:48
%S A356115 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 A356115 93,185,80,36,15,1,0,22,196,462,490,161,77,21,1,0,33,312,1120,1834,
%U A356115 1050,336,148,28,1
%N 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.
%H A356115 Peter Luschny, <a href="https://github.com/PeterLuschny/PermutationsWithLehmer/blob/main/PermutationsWithLehmer.ipynb">Permutations with Lehmer</a>, a SageMath Jupyter Notebook.
%e A356115 [ 1] [1]
%e A356115 [ 2] [0,  1]
%e A356115 [ 3] [0,  1,   1]
%e A356115 [ 4] [0,  3,   1,    1]
%e A356115 [ 5] [0,  4,   6,    3,    1]
%e A356115 [ 6] [0,  9,  20,    6,    6,    1]
%e A356115 [ 7] [0, 11,  45,   50,   15,   10,   1]
%e A356115 [ 8] [0, 19,  93,  185,   80,   36,  15,   1]
%e A356115 [ 9] [0, 22, 196,  462,  490,  161,  77,  21,  1]
%e A356115 [10] [0, 33, 312, 1120, 1834, 1050, 336, 148, 28, 1]
%o A356115 (SageMath) # uses function reduce_partition_triangle from A356265.
%o A356115 def A356115_row(n: int) -> list[int]:
%o A356115     return reduce_partition_triangle(A356266_row, n + 1)[n - 1]
%o A356115 def A356115(n: int, k: int) -> int:
%o A356115     return A356115_row(n)[k]
%o A356115 for n in range(1, 11):
%o A356115     print([n], A356115_row(n))
%Y A356115 Cf. A356266 (partition version), A356265, A120588 (row sums).
%K A356115 nonn,tabl
%O A356115 1,8
%A A356115 _Peter Luschny_, Aug 16 2022