OFFSET
0,4
LINKS
Giulio Cerbai and Anders Claesson, Caylerian polynomials, arXiv:2310.01270 [math.CO], 2023. See p. 11.
Giulio Cerbai and Anders Claesson, Enumerative aspects of Caylerian polynomials, arXiv:2411.08426 [math.CO], 2024. See p. 2.
EXAMPLE
Triangle begins:
1
1
1 2
1 8 4
1 24 42 8
1 64 276 184 16
...
Because polynomials are: 1; 1; 1 + 2t; 1 + 8t + 4t^2; 1 + 24t + 42t^2 + 8t^3; 1 + 64t + 276t^2 + 184t^3 + 16t^4; ...
PROG
(Python)
from itertools import product
def cayley_permutations(n):
return [p for p in product(range(n), repeat=n) if len(set(p)) == max(p)+1]
for n in range(1, 9):
a = [0] * n
for p in cayley_permutations(n):
a[sum(x>y for x, y in zip(p, p[1:]))] += 1
print(a[::-1]) # Andrei Zabolotskii, Jul 26 2025
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Oct 03 2023
EXTENSIONS
Rows 6-9 from Andrei Zabolotskii, Jul 26 2025
STATUS
approved
