A335797 a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k!).

1, 1, 1, 4, 5, 51, 7, 876, 457, 7678, 5271, 678569, 10705, 27644436, 5060161, 133924576, 197920145, 82864869803, 173283535, 5832742205056, 98269310261, 34660429169122, 25313714237505, 44152005855084345, 13685698802401, 2410161938206898126, 129066382491033573

Offset: 0

Author

Ilya Gutkovskiy, Oct 12 2020

Keywords

• nonn

Comments

Number of set partitions of [n] into blocks that are relatively prime to n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..576

Crossrefs

Cf. A057562, A275429, A335088.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1, add(`if`(
      igcd(j, m)=1, b(n-j, m), 0)*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..27);  # 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, 26}]