a(n) = n! * Sum_{k=0..n} binomial(k+4,n-k) / k!.

Terms

a(0) =1a(1) =5a(2) =23a(3) =103a(4) =473a(5) =2261a(6) =11215a(7) =57863a(8) =309713a(9) =1715653a(10) =9831911a(11) =58058375a(12) =353546473a(13) =2210900693a(14) =14215319903a(15) =93610866151a(16) =632159025185