L.g.f.: -log( Sum_{n=-oo..+oo} (-p)^n * (p*x)^(n^2) ) = Sum_{n>=1} a(n) * x^n/n, where p = sqrt(2).

Terms

a(0) =3a(1) =9a(2) =27a(3) =41a(4) =93a(5) =189a(6) =297a(7) =481a(8) =1161a(9) =1809a(10) =3105a(11) =6449a(12) =10689a(13) =20673a(14) =44577a(15) =73217a(16) =144129a(17) =299457a(18) =553473a(19) =1107201a(20) =2243457a(21) =4299777a(22) =8529921a(23) =17203969a(24) =34030593a(25) =67604481a(26) =136001025a(27) =269709313a(28) =538296321a(29) =1081023489