a(n) = (n!+5)/5.

Terms

a(0) =25a(1) =145a(2) =1009a(3) =8065a(4) =72577a(5) =725761a(6) =7983361a(7) =95800321a(8) =1245404161a(9) =17435658241a(10) =261534873601