a(n) = 1 + Sum_{k=0..n-2} binomial(n-2,k) * a(k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =14a(6) =36a(7) =101a(8) =308a(9) =1013a(10) =3562a(11) =13300a(12) =52482a(13) =218045a(14) =950614a(15) =4335563a(16) =20628882a(17) =102153978a(18) =525383324a(19) =2801105889a(20) =15455435864a(21) =88117352141a(22) =518391612686