a(n) = A000217(A342930(n))/n^n.

Terms

a(0) =1a(1) =7a(2) =13a(3) =511a(4) =1562a(5) =3013a(6) =411771a(7) =33554431a(8) =193710244a(9) =159687996a(10) =142655835305