a(n) = n! * Sum_{k=0..n} k^5 / k!.

Terms

a(0) =0a(1) =1a(2) =34a(3) =345a(4) =2404a(5) =15145a(6) =98646a(7) =707329a(8) =5691400a(9) =51281649a(10) =512916490a(11) =5642242441a(12) =67707158124a(13) =880193426905