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A244401 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 5.

%I A244401 #9 Feb 09 2015 10:55:52
%S A244401 1,2,6,17,50,142,409,1169,3356,9617,27601,79210,227527,653793,1879867,
%T A244401 5407806,15564968,44820889,129127761,372177974,1073169150,3095721985,
%U A244401 8933568154,25789862435,74477871565,215155604291,621754458752,1797297119000,5196966140656
%N A244401 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 5.
%H A244401 Alois P. Heinz, <a href="/A244401/b244401.txt">Table of n, a(n) for n = 6..1000</a>
%F A244401 a(n) = A036721(n) - A036718(n).
%p A244401 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244401       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244401        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244401     end:
%p A244401 a:= n-> b(n-1$2, 5$2) -`if`(k=0, 0, b(n-1$2, 4$2)):
%p A244401 seq(a(n), n=6..40);
%t A244401 b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]* b[n - i*j, i - 1, t - j, k], {j, 0, Min[t, n/i]}]] // FullSimplify] ; a[n_] := b[n-1, n-1, 5, 5] - If[n == 0, 0, b[n-1, n-1, 4, 4]]; Table[a[n], {n, 6, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244401 Column k=5 of A244372.
%Y A244401 Cf. A036718, A036721.
%K A244401 nonn
%O A244401 6,2
%A A244401 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014