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A244400 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 4.

%I A244400 #9 Feb 09 2015 10:55:59
%S A244400 1,2,6,17,49,136,386,1081,3044,8549,24052,67642,190426,536205,1510920,
%T A244400 4259418,12014682,33907056,95740913,270468869,764450150,2161638413,
%U A244400 6115252839,17307553766,49005101669,138811296158,393351362321,1115072623713,3162183392471
%N A244400 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 4.
%H A244400 Alois P. Heinz, <a href="/A244400/b244400.txt">Table of n, a(n) for n = 5..1000</a>
%F A244400 a(n) = A036718(n) - A000598(n).
%p A244400 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244400       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244400        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244400     end:
%p A244400 a:= n-> b(n-1$2, 4$2) -`if`(k=0, 0, b(n-1$2, 3$2)):
%p A244400 seq(a(n), n=5..40);
%t A244400 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, 4, 4] - If[n == 0, 0, b[n-1, n-1, 3, 3]]; Table[a[n], {n, 5, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244400 Column k=4 of A244372.
%Y A244400 Cf. A000598, A036718.
%K A244400 nonn
%O A244400 5,2
%A A244400 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014