a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*C(n-k,k+1)/(n-k) * a(k), with a(0)=1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =17a(7) =38a(8) =92a(9) =238a(10) =643a(11) =1790a(12) =5076a(13) =14573a(14) =42241a(15) =123484a(16) =364052a(17) =1082602a(18) =3247759a(19) =9829820a(20) =30019326a(21) =92517644a(22) =287805801a(23) =903822922a(24) =2865339252a(25) =9168572009a(26) =29601077285a(27) =96377791839a(28) =316264456921