a(n)=Sum((A008292(n - j, j) - C(n - j - 1, j))/2, j=0, [(n - 1)/2]).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =4a(6) =15a(7) =56a(8) =214a(9) =854a(10) =3607a(11) =16172a(12) =76853a(13) =386082a(14) =2044198a(15) =11373124a(16) =66300473a(17) =403939612a(18) =2566116299a(19) =16962629860a(20) =116452790838a(21) =828903740138