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

Terms

a(0) =1a(1) =5a(2) =20a(3) =75a(4) =275a(5) =1001a(6) =3640a(7) =13260a(8) =48450a(9) =177650a(10) =653752a(11) =2414425a(12) =8947575a(13) =33266625a(14) =124062000a(15) =463991880a(16) =1739969550a(17) =6541168950a(18) =24647883000a(19) =93078189750a(20) =352207870014