Number of 1-2-3 trees with n edges and with thinning limbs.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =20a(6) =48a(7) =116a(8) =288a(9) =724a(10) =1849a(11) =4768a(12) =12423a(13) =32628a(14) =86342a(15) =229952a(16) =616042a(17) =1659012a(18) =4489101a(19) =12199521a(20) =33284546a(21) =91140797a(22) =250396629a(23) =690043032a(24) =1907022197a(25) =5284167884a(26) =14677681554a(27) =40862469713a(28) =114001697975