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A374292
Number of permutations of [n] such that the number of cycles of length k is zero or a divisor of k for every k.
5
1, 1, 1, 5, 17, 89, 474, 3324, 28440, 253448, 2476700, 26876420, 328110540, 4207321260, 58468831680, 877439227560, 14214209548560, 239870470655760, 4285924637475600, 81381169697904720, 1636049164466934000, 34301061146870607600, 750389221227585139200
OFFSET
0,4
LINKS
Wikipedia, Permutation
EXAMPLE
a(3) = 5: (1)(2,3), (1,2)(3), (1,3)(2), (1,2,3), (1,3,2).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(j=0 or irem(i, j)=0, b(n-i*j, i-1)*(i-1)!^j/j!*
combinat[multinomial](n, i$j, n-i*j), 0), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 02 2024
STATUS
approved