a(n) = Sum_{k=0..n} (-1)^k * 2^k * q(k), where q(k) is A000009 (partitions into distinct parts).

Terms

a(0) =1a(1) =-1a(2) =3a(3) =-13a(4) =19a(5) =-77a(6) =179a(7) =-461a(8) =1075a(9) =-3021a(10) =7219a(11) =-17357a(12) =44083a(13) =-103373a(14) =257075a(15) =-627661a(16) =1469491a(17) =-3511245a(18) =8547379a(19) =-19764173a(20) =47344691a(21) =-112038861a(22) =261254195a(23) =-611161037a(24) =1435659315a(25) =-3329070029a(26) =7743892531a(27) =-18025911245a(28) =41566759987a(29) =-95872193485