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

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =5a(5) =13a(6) =56a(7) =223a(8) =1056a(9) =5243a(10) =28401a(11) =163578a(12) =1003332a(13) =6506149a(14) =44464510a(15) =319066188a(16) =2396942740a(17) =18800878491a(18) =153611297283