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A292555 Number of rooted unlabeled trees on n nodes where each node has at most 10 children. 11
1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4765, 12483, 32964, 87785, 235305, 634628, 1720524, 4686842, 12820920, 35206475, 97010705, 268154003, 743351390, 2066090876, 5756490561, 16074597300, 44980514021, 126109353817, 354202275766, 996517941454 (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..10} 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_10)(T(z)).

a(n) = Sum_{j=1..10} 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, 10$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, 10, 10]];

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, A292554, A292556.

Column k=10 of A299038.

Sequence in context: A255640 A216403 A145548 * A318804 A318857 A145549

Adjacent sequences:  A292552 A292553 A292554 * A292556 A292557 A292558

KEYWORD

nonn

AUTHOR

Marko Riedel, Sep 18 2017

STATUS

approved

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Last modified November 15 03:35 EST 2018. Contains 317224 sequences. (Running on oeis4.)