cp's OEIS Frontend

A229394 Number of shapes of balanced 9-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 A229394 #11 Dec 29 2014 18:10:51
%S A229394 1,1,9,36,84,126,126,84,36,9,1,81,2916,61236,826686,7440174,44641044,
%T A229394 172186884,387420489,387420489,13947137604,223154201664,2082772548864,
%U A229394 12496635293184,49986541172736,133297443127296,228509902503936,228509902503936,101559956668416
%N A229394 Number of shapes of balanced 9-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 A229394 a(n) = 1 for n in { A002452 }.
%H A229394 Alois P. Heinz, <a href="/A229394/b229394.txt">Table of n, a(n) for n = 0..820</a>
%p A229394 a:= proc(n) option remember; local m, r; if n<2 then 1 else
%p A229394       r:= iquo(n-1, 9, 'm'); binomial(9, m) *a(r+1)^m *a(r)^(9-m) fi
%p A229394     end:
%p A229394 seq(a(n), n=0..91);
%Y A229394 Column k=9 of A221857.
%Y A229394 Cf. A175673.
%K A229394 nonn,look
%O A229394 0,3
%A A229394 _Alois P. Heinz_, Sep 21 2013