Expansion of solution of functional equation.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =43a(6) =142a(7) =495a(8) =1794a(9) =6683a(10) =25388a(11) =97852a(12) =381406a(13) =1500317a(14) =5947798a(15) =23739795a(16) =95326150a(17) =384845581a(18) =1561220986a(19) =6361205709a(20) =26021379044a(21) =106826116871a(22) =439987835410