a(n) = OP(sum{i=0,...,n} OP(binomial(n,i))), where OP(n) is the odd part of n (A000265).

Terms

a(0) =1a(1) =1a(2) =3a(3) =1a(4) =7a(5) =11a(6) =43a(7) =1a(8) =67a(9) =103a(10) =405a(11) =157a(12) =1603a(13) =2627a(14) =10819a(15) =1a(16) =11427a(17) =18395a(18) =73273a(19) =27099a(20) =245929a(21) =385333a(22) =1516069a(23) =8955a(24) =3288479a(25) =5588411a(26) =24411113a(27) =9596521a(28) =104620147a(29) =171729011