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

0,8

Links

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

Example

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

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);

Crossrefs

Cf. A000081, A004111, A303023.

Sequence in context: A000621 A191317 A218020 * A039828 A357303 A246360

Adjacent sequences: A318517 A318518 A318519 * A318521 A318522 A318523

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2018

Status

approved