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.

1, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 100, 4500, 120000, 2100000, 25200000, 210000000, 1200000000, 4500000000, 10000000000, 10000000000, 450000000000, 9112500000000, 109350000000000, 861131250000000, 4650108750000000, 17437907812500000

Offset: 0

Author

Alois P. Heinz, Sep 21 2013

Keywords

• nonn
• look

Comments

a(n) = 1 for n in { A002275 }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1111

Crossrefs

Column k=10 of A221857.

Programs

Maple

a:= proc(n) option remember; local m, r; if n<2 then 1 else
      r:= iquo(n-1, 10, 'm'); binomial(10, m) *a(r+1)^m *a(r)^(10-m) fi
    end:
seq(a(n), n=0..111);