G.f.: exp( Sum_{n>=1} (x^n/n)/sqrt(1 - 2*(2*x)^n) ).

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =33a(5) =115a(6) =445a(7) =1653a(8) =6445a(9) =24783a(10) =97181a(11) =379105a(12) =1495607a(13) =5884239a(14) =23289639a(15) =92143819a(16) =365700023a(17) =1451737985a(18) =5774284819a(19) =22976698471a(20) =91541016133a(21) =364883522809