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

Terms

a(0) =1a(1) =1a(2) =4a(3) =7a(4) =51a(5) =16a(6) =876a(7) =2045a(8) =15475a(9) =15256a(10) =678569a(11) =2006863a(12) =27644436a(13) =46065293a(14) =669225640a(15) =5235101739a(16) =82864869803a(17) =234937438645