Let f[n]=Prime[n+1]-Prime[n]; a(n) = Binomial[Prime[12],f[n]].

Terms

a(0) =37a(1) =666a(2) =666a(3) =66045a(4) =666a(5) =66045a(6) =666a(7) =66045a(8) =2324784a(9) =666a(10) =2324784a(11) =66045a(12) =666a(13) =66045a(14) =2324784a(15) =2324784a(16) =666a(17) =2324784a(18) =66045a(19) =666a(20) =2324784a(21) =66045a(22) =2324784a(23) =38608020a(24) =66045a(25) =666a(26) =66045a(27) =666a(28) =66045a(29) =6107086800