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A244402 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 6.

%I A244402 #9 Feb 09 2015 10:55:45
%S A244402 1,2,6,17,50,143,415,1192,3444,9931,28687,82857,239563,692878,2005381,
%T A244402 5806915,16824277,48767953,141430699,410341703,1191064873,3458607705,
%U A244402 10046993035,29196507434,84874753458,246814998803,717965190047,2089140528083,6080768466919
%N A244402 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 6.
%H A244402 Alois P. Heinz, <a href="/A244402/b244402.txt">Table of n, a(n) for n = 7..1000</a>
%F A244402 a(n) = A036722(n) - A036721(n).
%p A244402 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244402       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244402        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244402     end:
%p A244402 a:= n-> b(n-1$2, 6$2) -`if`(k=0, 0, b(n-1$2, 5$2)):
%p A244402 seq(a(n), n=7..40);
%t A244402 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, 6, 6] - If[n == 0, 0, b[n - 1, n - 1, 5, 5]]; Table[a[n], {n, 7, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244402 Column k=6 of A244372.
%Y A244402 Cf. A036721, A036722.
%K A244402 nonn
%O A244402 7,2
%A A244402 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014