Coefficient of x^n in g.f.^n is A086608(n).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =6a(6) =12a(7) =29a(8) =64a(9) =114a(10) =404a(11) =641a(12) =2637a(13) =3289a(14) =15853a(15) =22068a(16) =98168a(17) =164238a(18) =547111a(19) =1292502a(20) =3020056a(21) =10442124a(22) =15954682a(23) =79385179a(24) =89229089a(25) =576106142a(26) =595912173a(27) =3848976774a(28) =4853522881a(29) =23699101223