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A229395 Number of shapes of balanced 10-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 A229395 #8 Jun 26 2014 13:40:17
%S A229395 1,1,10,45,120,210,252,210,120,45,10,1,100,4500,120000,2100000,
%T A229395 25200000,210000000,1200000000,4500000000,10000000000,10000000000,
%U A229395 450000000000,9112500000000,109350000000000,861131250000000,4650108750000000,17437907812500000
%N A229395 Number of shapes of balanced 10-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 A229395 a(n) = 1 for n in { A002275 }.
%H A229395 Alois P. Heinz, <a href="/A229395/b229395.txt">Table of n, a(n) for n = 0..1111</a>
%p A229395 a:= proc(n) option remember; local m, r; if n<2 then 1 else
%p A229395       r:= iquo(n-1, 10, 'm'); binomial(10, m) *a(r+1)^m *a(r)^(10-m) fi
%p A229395     end:
%p A229395 seq(a(n), n=0..111);
%Y A229395 Column k=10 of A221857.
%K A229395 nonn,look
%O A229395 0,3
%A A229395 _Alois P. Heinz_, Sep 21 2013