a(n) = [x^n] 1/(Sum_{k>=0} x^(k^2))^n.

Terms

a(0) =1a(1) =-1a(2) =3a(3) =-10a(4) =31a(5) =-96a(6) =294a(7) =-876a(8) =2511a(9) =-6796a(10) =16698a(11) =-33540a(12) =31174a(13) =184534a(14) =-1627812a(15) =8912760a(16) =-41466433a(17) =176963760a(18) =-714194382a(19) =2766892840a(20) =-10374065814a(21) =37815483948a(22) =-134334781732a(23) =465432203640