a(n) = Sum_{k=0..floor((n-2)/3)} 2^k * Stirling2(n,3*k+2).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =17a(6) =61a(7) =343a(8) =2231a(9) =14301a(10) =88561a(11) =542011a(12) =3397483a(13) =22638993a(14) =164336085a(15) =1299899087a(16) =10991061663a(17) =97070035205a(18) =881323166809