G.f.: Sum_{n>=0} x^(n*(n+1)/2) * P(x)^n, where P(x) is the partition function (A000041).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =10a(6) =18a(7) =34a(8) =60a(9) =109a(10) =192a(11) =339a(12) =591a(13) =1027a(14) =1768a(15) =3032a(16) =5165a(17) =8755a(18) =14766a(19) =24786a(20) =41417a(21) =68912a(22) =114193a(23) =188478a(24) =309939a(25) =507821a(26) =829197a(27) =1349437a(28) =2189105a(29) =3540253