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A330432
Number of permutations sigma of [n] such that k * sigma(k) >= n for 1 <= k <= n.
2
1, 1, 1, 1, 2, 4, 18, 54, 384, 1920, 15000, 108000, 1270080, 8890560, 126443520, 1440270720, 18811699200, 232243200000, 4303470124800, 56336336179200, 1165698293760000, 17784994106880000, 349410939842764800, 6977881195084800000, 173541988447027200000
OFFSET
0,5
COMMENTS
sigma(1) = n and sigma(n) = 1.
EXAMPLE
In case of n = 4.
----+-------------
1 | [4, 2, 3, 1]
2 | [4, 3, 2, 1]
In case of n = 5.
----+----------------
1 | [5, 3, 2, 4, 1]
2 | [5, 3, 4, 2, 1]
3 | [5, 4, 2, 3, 1]
4 | [5, 4, 3, 2, 1]
PROG
(Ruby)
def A(n)
(2..n - 1).to_a.permutation.select{|i| (2..n - 1).all?{|j| i[j - 2] * j >= n}}.size
end
def A330432(n)
(0..n).map{|i| A(i)}
end
p A330432(10)
CROSSREFS
Sequence in context: A301802 A318249 A093045 * A317887 A083694 A179040
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 01 2020
EXTENSIONS
a(16)-a(24) from Giovanni Resta, Mar 03 2020
STATUS
approved