a(n) = Sum_{k=0..floor(n/5)} Stirling2(n,5*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =15a(7) =140a(8) =1050a(9) =6951a(10) =42526a(11) =246785a(12) =1381105a(13) =7547826a(14) =40827787a(15) =223429571a(16) =1289945660a(17) =8411093621a(18) =66070626548a(19) =624900235273