a(n) = 2 + (89040 + (71868 + (29932 + (8449 + (1960 + (322 + (28 + n)*n)*n)*n)*n)*n)*n)*n/40320.

Terms

a(0) =2a(1) =7a(2) =25a(3) =81a(4) =236a(5) =622a(6) =1498a(7) =3334a(8) =6931a(9) =13586a(10) =25312a(11) =45124a(12) =77403a(13) =128351a(14) =206551a(15) =323647a(16) =495160a(17) =741457a(18) =1088891a(19) =1571131a(20) =2230702a(21) =3120756a(22) =4307096a(23) =5870476a(24) =7909201a(25) =10542052a(26) =13911562a(27) =18187670a(28) =23571781a(29) =30301261