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

%I A335797 #28 Oct 14 2020 14:51:30
%S A335797 1,1,1,4,5,51,7,876,457,7678,5271,678569,10705,27644436,5060161,
%T A335797 133924576,197920145,82864869803,173283535,5832742205056,98269310261,
%U A335797 34660429169122,25313714237505,44152005855084345,13685698802401,2410161938206898126,129066382491033573
%N A335797 a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k!).
%C A335797 Number of set partitions of [n] into blocks that are relatively prime to n.
%H A335797 Alois P. Heinz, <a href="/A335797/b335797.txt">Table of n, a(n) for n = 0..576</a>
%p A335797 b:= proc(n, m) option remember; `if`(n=0, 1, add(`if`(
%p A335797       igcd(j, m)=1, b(n-j, m), 0)*binomial(n-1, j-1), j=1..n))
%p A335797     end:
%p A335797 a:= n-> b(n$2):
%p A335797 seq(a(n), n=0..27);  # _Alois P. Heinz_, Oct 12 2020
%t A335797 Table[n! SeriesCoefficient[Exp[Sum[Boole[GCD[n, k] == 1] x^k/k!, {k, 1, n}]], {x, 0, n}], {n, 0, 26}]
%Y A335797 Cf. A057562, A275429, A335088.
%K A335797 nonn
%O A335797 0,4
%A A335797 _Ilya Gutkovskiy_, Oct 12 2020