L.g.f.: (-1/3)*log( Sum_{n>=0} (2*n+1)*(-x)^(n*(n+1)/2) ).

Terms

a(0) =1a(1) =3a(2) =14a(3) =47a(4) =156a(5) =524a(6) =1800a(7) =6159a(8) =20999a(9) =71638a(10) =244608a(11) =835124a(12) =2850836a(13) =9732012a(14) =33223314a(15) =113417951a(16) =387185490a(17) =1321771895a(18) =4512261114a(19) =15403943682a(20) =52585931706a(21) =179517678728a(22) =612836866428