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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =5a(5) =51a(6) =7a(7) =876a(8) =457a(9) =7678a(10) =5271a(11) =678569a(12) =10705a(13) =27644436a(14) =5060161a(15) =133924576a(16) =197920145a(17) =82864869803a(18) =173283535a(20) =98269310261