a(n) = Sum_{k=1..n} floor(n/k) * (-4)^(k-1).

Terms

a(0) =1a(1) =-2a(2) =15a(3) =-52a(4) =205a(5) =-806a(6) =3291a(7) =-13160a(8) =52393a(9) =-209498a(10) =839079a(11) =-3356300a(12) =13420917a(13) =-53683854a(14) =214751875a(15) =-859006400a(16) =3435960897a(17) =-13743843762a(18) =54975632975a(19) =-219902535924a(20) =879609095965