# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a048816 Showing 1-1 of 1 %I A048816 #39 May 15 2019 05:54:58 %S A048816 1,1,2,3,5,7,12,17,28,42,68,103,168,260,420,665,1075,1716,2787,4489, %T A048816 7304,11849,19333,31504,51561,84347,138378,227096,373445,614441, %U A048816 1012583,1669774,2756951,4555183,7533988,12469301,20655523,34238310,56795325,94270949 %N A048816 Number of rooted trees with n nodes with every leaf at the same height. %C A048816 The trees are unordered (see A000081). For balanced ordered rooted trees see A079500. - _Joerg Arndt_, Jul 20 2014 %C A048816 The trees are unlabeled. For labeled version see A238372. - _Alois P. Heinz_, Dec 29 2014 %H A048816 Vaclav Kotesovec, Table of n, a(n) for n = 1..3500 (terms 1..300 from Alois P. Heinz) %H A048816 Joerg Arndt, balanced unordered rooted trees for n = 1..10 %H A048816 Index entries for sequences related to rooted trees %e A048816 See Arndt link. %e A048816 From _Gus Wiseman_, Oct 08 2018: (Start) %e A048816 The a(1) = 1 through a(7) = 12 balanced rooted trees with n nodes: %e A048816 o (o) (oo) (ooo) (oooo) (ooooo) (oooooo) %e A048816 ((o)) ((oo)) ((ooo)) ((oooo)) ((ooooo)) %e A048816 (((o))) (((oo))) (((ooo))) (((oooo))) %e A048816 ((o)(o)) ((o)(oo)) ((o)(ooo)) %e A048816 ((((o)))) ((((oo)))) ((oo)(oo)) %e A048816 (((o)(o))) ((((ooo)))) %e A048816 (((((o))))) (((o)(oo))) %e A048816 ((o)(o)(o)) %e A048816 (((((oo))))) %e A048816 ((((o)(o)))) %e A048816 (((o))((o))) %e A048816 ((((((o)))))) %e A048816 (End) %t A048816 T[n_, k_] := T[n, k] = If[n==1, 1, If[k==0, 0, Sum[Sum[If[d