a(n) = n! * Sum_{k=0..floor(n/3)} 1 / (3*k)!.

Terms

a(0) =1a(1) =1a(2) =2a(3) =7a(4) =28a(5) =140a(6) =841a(7) =5887a(8) =47096a(9) =423865a(10) =4238650a(11) =46625150a(12) =559501801a(13) =7273523413a(14) =101829327782