A330432 Number of permutations sigma of [n] such that k * sigma(k) >= n for 1 <= k <= n.

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

Author

Seiichi Manyama, Mar 01 2020

Keywords

• nonn

Comments

sigma(1) = n and sigma(n) = 1.

Examples

			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]
		

Programs

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)

Extensions

a(16)-a(24) from Giovanni Resta, Mar 03 2020