login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292556 Number of rooted unlabeled trees on n nodes where each node has at most 11 children. 11
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

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-Fran├žois 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 A000081 A123467

Adjacent sequences:  A292553 A292554 A292555 * A292557 A292558 A292559

KEYWORD

nonn

AUTHOR

Marko Riedel, Sep 18 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 19:34 EDT 2018. Contains 316401 sequences. (Running on oeis4.)