a(n) = Sum(psi(k-1)*psi(n-k-1),k=0..n)+(1-(-1)^n)/2, where psi(k) = A000931(k+6).

Terms

a(0) =1a(1) =3a(2) =3a(3) =7a(4) =9a(5) =15a(6) =22a(7) =33a(8) =48a(9) =71a(10) =101a(11) =147a(12) =208a(13) =297a(14) =419a(15) =591a(16) =829a(17) =1161a(18) =1619a(19) =2255a(20) =3130a(21) =4339a(22) =6000a(23) =8285a(24) =11419a(25) =15717a(26) =21600a(27) =29649a(28) =40645a(29) =55659