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A292212 Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than six. 2

%I

%S 0,1,1,2,5,12,33,89,258,756,2279,6957,21592,67689,214451,684850,

%T 2203384,7133042,23222003,75971636,249646198,823597534,2726859943,

%U 9057797752,30176758016,100810029178,337614951216,1133292965615,3812333876764,12849946139206

%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than six.

%H Alois P. Heinz, <a href="/A292212/b292212.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

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

%p `if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,

%p `if`(v=n, 1, add(binomial(a(i)+j-1, j)*

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

%p end:

%p a:= proc(n) option remember; `if`(n<2, n,

%p add(b(n, n+1-j, j), j=2..min(n, 6)))

%p end:

%p seq(a(n), n=0..35);

%Y Column k=6 of A292085.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Sep 11 2017

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Last modified March 23 02:51 EDT 2019. Contains 321422 sequences. (Running on oeis4.)