A229394 - OEIS

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.

1, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 81, 2916, 61236, 826686, 7440174, 44641044, 172186884, 387420489, 387420489, 13947137604, 223154201664, 2082772548864, 12496635293184, 49986541172736, 133297443127296, 228509902503936, 228509902503936, 101559956668416

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OFFSET

0,3

COMMENTS

a(n) = 1 for n in { A002452 }.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..820

MAPLE

a:= proc(n) option remember; local m, r; if n<2 then 1 else

r:= iquo(n-1, 9, 'm'); binomial(9, m) *a(r+1)^m *a(r)^(9-m) fi

end:

seq(a(n), n=0..91);