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

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =26a(5) =96a(6) =356a(7) =1331a(8) =5014a(9) =19006a(10) =72412a(11) =277058a(12) =1063856a(13) =4097510a(14) =15823432a(15) =61245987a(16) =237536326a(17) =922906150a(18) =3591500972a(19) =13996328322a(20) =54614894396a(21) =213360770840a(22) =834409399672