Binomial(n-k-1,k) * binomial(n-k,k+1) where k = ceiling(n/4).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =6a(5) =1a(6) =12a(7) =60a(8) =200a(9) =150a(10) =700a(11) =2450a(12) =7056a(13) =8820a(14) =31752a(15) =97020a(16) =261360a(17) =426888a(18) =1359072a(19) =3864861a(20) =10020010a(21) =19324305a(22) =57257200a(23) =155739584a(24) =393853824a(25) =851005584a(26) =2405321568a(27) =6347376360a(28) =15774544800a(29) =37026362100