A318520 Number of unlabeled rooted identity trees with n non-binary nodes.

0, 1, 1, 1, 1, 1, 1, 2, 3, 5, 8, 14, 23, 40, 69, 122, 215, 382, 679, 1217, 2185, 3944, 7136, 12958, 23578, 43026, 78673, 144190, 264755, 487074, 897549, 1656697, 3062423, 5669110, 10508397, 19503447, 36240898, 67418514, 125551221, 234047825, 436722486

Offset: 0

Author

Alois P. Heinz, Aug 28 2018

Keywords

• nonn

Examples

			a(8) = 3:    o      o        o
             |      |       /|\
             o      o      o o o
             |     /|\     | |
             o    o o o    o o
             |    | |      |
             o    o o      o
             |    |        |
             o    o        o
             |
             o
             |
             o
             |
             o
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3501

Crossrefs

Cf. A000081, A004111, A303023.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=1, 0, 1), `if`(i<1, 0,
      add(b(n-i*j, i-1, max(0, t-j))*binomial(a(i), j), j=0..n/i)))
    end:
a:= n-> `if`(n<2, n, b(n-1$2, 3)):
seq(a(n), n=0..50);