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

%I

%S 1,1,1,2,4,9,20,48,115,286,719,1842,4766,12485,32970,87802,235355,

%T 634771,1720940,4688041,12824394,35216524,97039824,268238379,

%U 743596131,2066801045,5758552717,16080588286,44997928902,126160000878,354349643101,996946927831

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

%H Alois P. Heinz, <a href="/A292556/b292556.txt">Table of n, a(n) for n = 0..1000</a>

%H Marko Riedel, <a href="https://math.stackexchange.com/questions/2434908/">Trees with bounded degree.</a>

%F 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

%F T(z) = 1 + z*Z(S_11)(T(z)).

%F a(n) = Sum_{j=1..11} A244372(n,j) for n>0, a(0) = 1. - _Alois P. Heinz_, Sep 20 2017

%p b:= proc(n, i, t, k) option remember; `if`(n=0, 1,

%p `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*

%p b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))

%p end:

%p a:= n-> `if`(n=0, 1, b(n-1$2, 11$2)):

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Sep 20 2017

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

%Y Column k=11 of A299038.

%K nonn,changed

%O 0,4

%A _Marko Riedel_, Sep 18 2017

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Last modified February 20 02:47 EST 2018. Contains 299357 sequences. (Running on oeis4.)