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A292556 Number of rooted unlabeled trees on n nodes where each node has at most 11 children. 10
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 (list; graph; refs; listen; history; text; internal format)
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

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

CROSSREFS

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

Sequence in context: A145548 A292555 A145549 * A145550 A000081 A123467

Adjacent sequences:  A292553 A292554 A292555 * A292557 A292558 A292559

KEYWORD

nonn

AUTHOR

Marko Riedel, Sep 18 2017

STATUS

approved

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Last modified December 11 19:09 EST 2017. Contains 295919 sequences.