A244401 - OEIS

%I #9 Feb 09 2015 10:55:52

%S 1,2,6,17,50,142,409,1169,3356,9617,27601,79210,227527,653793,1879867,

%T 5407806,15564968,44820889,129127761,372177974,1073169150,3095721985,

%U 8933568154,25789862435,74477871565,215155604291,621754458752,1797297119000,5196966140656

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

%H Alois P. Heinz, <a href="/A244401/b244401.txt">Table of n, a(n) for n = 6..1000</a>

%F a(n) = A036721(n) - A036718(n).

%p b:= proc(n, i, t, k) option remember; `if`(n=0, 1,

%p       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*

%p        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))

%p     end:

%p a:= n-> b(n-1$2, 5$2) -`if`(k=0, 0, b(n-1$2, 4$2)):

%p seq(a(n), n=6..40);

%t 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 Column k=5 of A244372.

%Y Cf. A036718, A036721.

%K nonn

%O 6,2

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014