a(n) = Sum_{k=1..n} Stirling2(n,k) * gcd(n,k).

Terms

a(0) =1a(1) =3a(2) =7a(3) =25a(4) =56a(5) =484a(6) =883a(7) =9643a(8) =32497a(9) =344277a(10) =678580a(11) =13364806a(12) =27644449a(13) =582379763a(14) =3257283507a(15) =28924878925a(16) =82864869820