A292556 Number of rooted unlabeled trees on n nodes where each node has at most 11 children.

1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12485, 32970, 87802, 235355, 634771, 1720940, 4688041, 12824394, 35216524, 97039824, 268238379, 743596131, 2066801045, 5758552717, 16080588286, 44997928902, 126160000878, 354349643101, 996946927831

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Marko Riedel, Trees with bounded degree.

Formula

Functional equation of g.f. is T(z) = z + z*Sum_{q=1..11} Z(S_q)(T(z)) with Z(S_q) the cycle index of the symmetric group.

Alternate FEQ is T(z) = 1 + z*Z(S_11)(T(z)).

a(n) = Sum_{j=1..11} A244372(n,j) for n > 0, a(0) = 1. - Alois P. Heinz, Sep 20 2017

Limit_{n->oo} a(n)/a(n+1) = 0.338324339068091181557475416836618315086769320447748735003402... - Robert A. Russell, Feb 11 2023

Maple

b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
      `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
    end:
a:= n-> `if`(n=0, 1, b(n-1$2, 11$2)):
seq(a(n), n=0..35);  # Alois P. Heinz, Sep 20 2017

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k]+j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := If[n == 0, 1, b[n-1, n-1, 11, 11]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 05 2018, after Alois P. Heinz *)

Crossrefs

Cf. A000081, A001190, A000598, A036718, A036721, A036722, A182378, A244372, A292553, A292554, A292555.

Column k=11 of A299038.

Sequence in context: A318804 A318857 A145549 * A145550 A123467 A000081

Adjacent sequences: A292553 A292554 A292555 * A292557 A292558 A292559

Keyword

nonn

Author

Marko Riedel, Sep 18 2017

Status

approved