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

Offset: 0

Author

Alois P. Heinz, Sep 21 2013

Keywords

• nonn
• look

Comments

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

Links

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

Crossrefs

Column k=9 of A221857.

Cf. A175673.

Programs

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);