A318818 Number of rooted trees with n nodes such that three equals the maximal number of subtrees of the same size extending from the same node.

0, 1, 1, 3, 9, 23, 60, 166, 447, 1219, 3344, 9214, 25493, 70853, 197150, 550259, 1539767, 4314746, 12112304, 34063256, 95904943, 270375031, 763193304, 2156328194, 6098563949, 17264760959, 48912296290, 138683094562, 393514686620, 1117304554815, 3174397805762

Offset

3,4

Links

Alois P. Heinz, Table of n, a(n) for n = 3..2158

Maple

g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
    end:
a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(3):
seq(a(n), n=3..33);

Crossrefs

Column k=3 of A318754.

Sequence in context: A323798 A180488 A318860 * A026599 A061647 A207008

Adjacent sequences: A318815 A318816 A318817 * A318819 A318820 A318821

Keyword

nonn

Author

Alois P. Heinz, Sep 04 2018

Status

approved