a(n) = 3*(n+1)*binomial(n+2,6).

Terms

a(0) =15a(1) =126a(2) =588a(3) =2016a(4) =5670a(5) =13860a(6) =30492a(7) =61776a(8) =117117a(9) =210210a(10) =360360a(11) =594048a(12) =946764a(13) =1465128a(14) =2209320a(15) =3255840a(16) =4700619a(17) =6662502a(18) =9287124a(19) =12751200a(20) =17267250a(21) =23088780a(22) =30515940a(23) =39901680a(24) =51658425a(25) =66265290a(26) =84275856a(27) =106326528a(28) =133145496a(29) =165562320