A335088 a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k).

1, 1, 1, 4, 9, 96, 145, 4320, 11025, 179200, 693441, 36288000, 62610625, 5748019200, 15259154625, 378002200576, 4108830350625, 334764638208000, 643373556450625, 115242726703104000, 309281197713168681, 14870534508544000000, 168541849294187630625

Offset: 0

Author

Ilya Gutkovskiy, Oct 12 2020

Keywords

• nonn

Comments

Number of permutations of [n] whose cycle lengths are relatively prime to n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A074759, A226388, A335797.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1, add(`if`(
      igcd(j, m)=1, b(n-j, m), 0)*(n-1)!/(n-j)!, j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);  # Alois P. Heinz, Oct 12 2020

Mathematica

Table[n! SeriesCoefficient[Exp[Sum[Boole[GCD[n, k] == 1] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 22}]