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

Terms

a(0) =0a(1) =0a(2) =0a(3) =3a(4) =0a(5) =6a(6) =40a(7) =150a(8) =100a(9) =525a(10) =1960a(11) =5880a(12) =7056a(13) =26460a(14) =83160a(15) =228690a(16) =365904a(17) =1189188a(18) =3435432a(19) =9018009a(20) =17177160a(21) =51531480a(22) =141581440a(23) =361032672a(24) =773641440a(25) =2204878104a(26) =5859116640a(27) =14647791600a(28) =34178180400a(29) =93989996100