Product_{n>=1} (1 + x^n)^a(n) = g.f. of A005169 (fountains of coins).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =4a(6) =5a(7) =10a(8) =13a(9) =23a(10) =35a(11) =59a(12) =93a(13) =154a(14) =248a(15) =413a(16) =671a(17) =1111a(18) =1827a(19) =3036a(20) =5013a(21) =8348a(22) =13859a(23) =23122a(24) =38534a(25) =64434a(26) =107715a(27) =180509a(28) =302565a(29) =508032