a(n) = 280*C(n,9)+10*C(n,6)+6*C(n,4)+C(n,3)+1 where C = binomial.

Terms

a(0) =1a(1) =1a(2) =2a(3) =11a(4) =41a(5) =121a(6) =316a(7) =757a(8) =1961a(9) =6281a(10) =22166a(11) =74031a(12) =221937a(13) =596961a(14) =1460096a(15) =3294761a(16) =6945521a(17) =13818417a(18) =26161386a(19) =47446611a(20) =82880281a(21) =140069161a(22) =229877572a(23) =367512861a(24) =573882201a(25) =877268601a(26) =1315379326a(27) =1937825527a(28) =2809097761a(29) =4012108241