a(n) = Sum_{k=0..floor((n-2)/5)} Stirling2(n,5*k+2).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =15a(6) =31a(7) =64a(8) =155a(9) =717a(10) =6391a(11) =65010a(12) =629444a(13) =5719597a(14) =49340838a(15) =408864186a(16) =3284672489a(17) =25770192646a(18) =198718943490