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A292554 Number of rooted unlabeled trees on n nodes where each node has at most 9 children. 11
1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1841, 4763, 12477, 32947, 87735, 235162, 634212, 1719325, 4683368, 12810871, 35177357, 96926335, 267909285, 742641309, 2064029034, 5750500663, 16057186086, 44929879114, 125962026154, 353773417487, 995269027339 (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..9} 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_9)(T(z)).

a(n) = Sum_{j=1..9} 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, 9$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, 9, 9]];

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Jun 04 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A000081, A001190, A000598, A036718, A036721, A036722, A182378, A244372, A292553, A292555, A292556.

Column k=9 of A299038.

Sequence in context: A216062 A034826 A145547 * A318803 A318856 A255640

Adjacent sequences:  A292551 A292552 A292553 * A292555 A292556 A292557

KEYWORD

nonn

AUTHOR

Marko Riedel, Sep 18 2017

STATUS

approved

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Last modified September 18 11:42 EDT 2018. Contains 315130 sequences. (Running on oeis4.)