a(n) = (C(2n, n)/2 - (2^(n-1) + ((n+1) mod 2)*C(n-1, n/2-1)))/2.

Terms

a(0) =0a(1) =0a(2) =3a(3) =12a(4) =55a(5) =210a(6) =826a(7) =3136a(8) =12027a(9) =45870a(10) =175846a(11) =674784a(12) =2598102a(13) =10024196a(14) =38771188a(15) =150250496a(16) =583368787a(17) =2268706134a(18) =8836184878a(19) =34461323872a(20) =134563944322a(21) =526023515996