a(1)=1; for n > 1, a(n) = Sum_{1<=j<n, gcd(j,n)=1} a(j)*a(n-j).

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =12a(5) =24a(6) =88a(7) =224a(8) =720a(9) =1792a(10) =7200a(11) =16512a(12) =69952a(13) =185984a(14) =608896a(15) =1797120a(16) =7495424a(17) =17936896a(18) =79457792a(19) =211576832a(20) =742306816a(21) =2190231552a(22) =9482688512a(23) =23198867456a(24) =97967427584a(25) =285227057152