a(n) = 1/2*binomial(2*n,n) - (1+(-1)^n)/4*(binomial(n,floor(n/2)))^2.

Terms

a(0) =0a(1) =1a(2) =1a(3) =10a(4) =17a(5) =126a(6) =262a(7) =1716a(8) =3985a(9) =24310a(10) =60626a(11) =352716a(12) =925190a(13) =5200300a(14) =14168988a(15) =77558760a(16) =217721745a(17) =1166803110a(18) =3355615450a(19) =17672631900a(20) =51855874642a(21) =269128937220a(22) =803232328548