a(n) = 8*binomial(2*n+1,n-3)/(n+5).

Terms

a(0) =1a(1) =8a(2) =44a(3) =208a(4) =910a(5) =3808a(6) =15504a(7) =62016a(8) =245157a(9) =961400a(10) =3749460a(11) =14567280a(12) =56448210a(13) =218349120a(14) =843621600a(15) =3257112960a(16) =12570420330a(17) =48507033744a(18) =187187399448a(19) =722477682080