Number of forests of rooted trees where n dollars are spent and an n-node tree costs 2n-1 dollars.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =5a(6) =9a(7) =11a(8) =21a(9) =28a(10) =50a(11) =68a(12) =123a(13) =173a(14) =310a(15) =441a(16) =789a(17) =1147a(18) =2044a(19) =2999a(20) =5351a(21) =7938a(22) =14143a(23) =21138a(24) =37686a(25) =56729a(26) =101144a(27) =153085a(28) =273077a(29) =415407