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

0,3

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);

Crossrefs

Column k=9 of A221857.

Cf. A175673.

Sequence in context: A175673 A285198 A230212 * A173682 A009522 A045851

Adjacent sequences: A229391 A229392 A229393 * A229395 A229396 A229397

Keyword

nonn,look

Author

Alois P. Heinz, Sep 21 2013

Status

approved