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%I #6 Sep 12 2017 11:55:07
%S 1,2,7,23,78,262,892,3034,10379,35581,122338,421498,1455216,5032559,
%T 17431384,60460263,209967105,729996715,2540602259,8850326207,
%U 30857134567,107670278671,375970664930,1313731592633,4593388008873,16069958896737,56251584472388
%N Number of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that the maximum of the node outdegrees equals seven.
%H Alois P. Heinz, <a href="/A292233/b292233.txt">Table of n, a(n) for n = 7..1000</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%p b:= proc(n, i, v, k) 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, k)+j-1, j)*
%p b(n-i*j, i-1, v-j, k), j=0..min(n/i, v)))))
%p end:
%p A:= proc(n, k) option remember; `if`(n<2, n,
%p add(b(n, n+1-j, j, k), j=2..min(n, k)))
%p end:
%p a:= n-> A(n, 7)-A(n, 6):
%p seq(a(n), n=7..35);
%Y Column k=7 of A292086.
%K nonn
%O 7,2
%A _Alois P. Heinz_, Sep 12 2017
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