a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n-4*k,n-2*k).

Terms

a(0) =1a(1) =2a(2) =5a(3) =18a(4) =65a(5) =234a(6) =859a(7) =3198a(8) =12011a(9) =45422a(10) =172745a(11) =660010a(12) =2531411a(13) =9740590a(14) =37585189a(15) =145376930a(16) =563495201a(17) =2188229290a(18) =8511640099a(19) =33157034510a(20) =129334888721a(21) =505100839930