G.f.: A(x) = Product_{n>=1} G(x^n,n)^n where G(x,n) = 1 + x*G(x,n)^n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =15a(5) =26a(6) =66a(7) =110a(8) =253a(9) =460a(10) =966a(11) =1680a(12) =3732a(13) =6304a(14) =13073a(15) =23539a(16) =47548a(17) =82362a(18) =171463a(19) =293578a(20) =597934a(21) =1056830a(22) =2105424a(23) =3654919a(24) =7533609a(25) =12915780a(26) =26112978a(27) =46033557a(28) =92504870a(29) =160298673