a(n) = Sum_{k=0..n} (-1)^k * 2^k * p(k), where p(k) is the partition function A000041.

Terms

a(0) =1a(1) =-1a(2) =7a(3) =-17a(4) =63a(5) =-161a(6) =543a(7) =-1377a(8) =4255a(9) =-11105a(10) =31903a(11) =-82785a(12) =232607a(13) =-594785a(14) =1617055a(15) =-4150113a(16) =10988703a(17) =-27939681a(18) =72985759a(19) =-183915361a(20) =473541791a(21) =-1187402593a(22) =3015290015a(23) =-7512413025a(24) =18911702175a(25) =-46787875681a(26) =116689317023a(27) =-287306044257