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%I #11 Aug 28 2021 03:15:54
%S 1,0,0,0,0,5,11,12,13,14,50,136,289,477,703,1255,2611,5489,10902,
%T 19712,35455,66651,130014,254737,488041,920461,1741642,3338360,
%U 6453073,12425997,23780944,45451155,87224392,168253246,324863578,625728091,1202953325,2314485753
%N Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.
%H Alois P. Heinz, <a href="/A244534/b244534.txt">Table of n, a(n) for n = 6..1000</a>
%p b:= proc(n, t, k) option remember; `if`(n=0,
%p `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
%p b(n-j, max(0, t-1), k), j=1..n)))
%p end:
%p a:= n-> b(n-1, 5$2) -b(n-1, 6$2):
%p seq(a(n), n=6..50);
%t b[n_, t_, k_] := b[n, t, k] = If[n == 0,
%t If[MemberQ[{0, k}, t], 1, 0], If[t > n, 0, Sum[b[j-1, k, k]*
%t b[n-j, Max[0, t-1], k], {j, n}]]];
%t a[n_] := b[n-1, 5, 5] - b[n-1, 6, 6];
%t Table[a[n], {n, 6, 50}] (* _Jean-François Alcover_, Aug 28 2021, after Maple code *)
%Y Column k=5 of A244530.
%Y Cf. A244459.
%K nonn
%O 6,6
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014
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