a(n) = binomial(n,3)*binomial(n-1,3)/4.

Terms

a(0) =1a(1) =10a(2) =50a(3) =175a(4) =490a(5) =1176a(6) =2520a(7) =4950a(8) =9075a(9) =15730a(10) =26026a(11) =41405a(12) =63700a(13) =95200a(14) =138720a(15) =197676a(16) =276165a(17) =379050a(18) =512050a(19) =681835a(20) =896126a(21) =1163800a(22) =1495000a(23) =1901250a(24) =2395575a(25) =2992626a(26) =3708810a(27) =4562425a(28) =5573800a(29) =6765440