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A318859 Number of rooted trees with n nodes such that two equals the maximal number of isomorphic subtrees extending from the same node. 3

%I

%S 0,1,1,4,9,22,54,138,346,889,2285,5928,15436,40424,106230,280305,

%T 741912,1969816,5243942,13995807,37439883,100371907,269623436,

%U 725638613,1956352468,5283171593,14289645110,38707131195,104995130162,285184002486,775586517781

%N Number of rooted trees with n nodes such that two equals the maximal number of isomorphic subtrees extending from the same node.

%H Alois P. Heinz, <a href="/A318859/b318859.txt">Table of n, a(n) for n = 2..2213</a>

%p h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),

%p `if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))

%p end:

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

%p add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))

%p end:

%p A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):

%p a:= n-> (k-> A(n, k)-A(n, k-1))(2):

%p seq(a(n), n=2..32);

%Y Column k=2 of A318758.

%K nonn

%O 2,4

%A _Alois P. Heinz_, Sep 04 2018

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Last modified August 15 17:39 EDT 2022. Contains 356148 sequences. (Running on oeis4.)