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A229393 Number of shapes of balanced 8-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one.

%I A229393 #7 Sep 26 2013 06:45:29
%S A229393 1,1,8,28,56,70,56,28,8,1,64,1792,28672,286720,1835008,7340032,
%T A229393 16777216,16777216,469762048,5754585088,40282095616,176234168320,
%U A229393 493455671296,863547424768,863547424768,377801998336,6044831973376,42313823813632,169255295254528
%N A229393 Number of shapes of balanced 8-ary trees with n nodes, where a tree is balanced if the total number of nodes in subtrees corresponding to the branches of any node differ by at most one.
%C A229393 a(n) = 1 for n in { A023001 }.
%H A229393 Alois P. Heinz, <a href="/A229393/b229393.txt">Table of n, a(n) for n = 0..585</a>
%p A229393 a:= proc(n) option remember; local m, r; if n<2 then 1 else
%p A229393       r:= iquo(n-1, 8, 'm'); binomial(8, m) *a(r+1)^m *a(r)^(8-m) fi
%p A229393     end:
%p A229393 seq(a(n), n=0..73);
%Y A229393 Column k=8 of A221857.
%K A229393 nonn
%O A229393 0,3
%A A229393 _Alois P. Heinz_, Sep 21 2013