OFFSET
1,5
LINKS
Peter Luschny, Permutations with Lehmer, a SageMath Jupyter Notebook.
EXAMPLE
Triangle T(n, k) starts: [Row sums]
[1] [0] [0]
[2] [1, 0] [1]
[3] [1, 2, 0] [3]
[4] [1, 8, 2, 0] [11]
[5] [1, 21, 25, 2, 0] [49]
[6] [1, 49, 152, 55, 2, 0] [259]
[7] [1, 106, 697, 670, 117, 2, 0] [1593]
[8] [1, 223, 2756, 5493, 2509, 243, 2, 0] [11227]
[9] [1, 459, 9966, 36105, 33669, 8838, 497, 2, 0] [89537]
PROG
(SageMath) # uses function A356264_row
@cache
def Pn(n: int, k: int) -> int:
if k == 0: return 0
if n == 0 or k == 1: return 1
return Pn(n, k - 1) + Pn(n - k, k) if k <= n else Pn(n, k - 1)
def reduce_parts(fun, n: int) -> list[int]:
funn: list[int] = fun(n)
return [sum(funn[Pn(n, k):Pn(n, k + 1)]) for k in range(n)]
def reduce_partition_triangle(fun, n: int) -> list[list[int]]:
return [reduce_parts(fun, k) for k in range(1, n)]
def A356265_row(n: int) -> list[int]:
return reduce_partition_triangle(A356264_row, n+1)[n-1]
for n in range(1, 8):
print(A356265_row(n))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 16 2022
STATUS
approved