a(n) = Sum_{k=0..n-1} (-1)^k*A000172(k).

Terms

a(0) =0a(1) =1a(2) =-1a(3) =9a(4) =-47a(5) =299a(6) =-1953a(7) =13231a(8) =-91729a(9) =647433a(10) =-4633499a(11) =33531761a(12) =-244884159a(13) =1802040241a(14) =-13346305519a(15) =99392117841a(16) =-743734839215