cp's OEIS Frontend

A244459 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.

%I A244459 #9 Feb 06 2015 08:12:25
%S A244459 1,0,0,0,0,1,2,2,2,2,4,7,12,16,21,29,43,65,99,142,206,297,436,641,945,
%T A244459 1383,2029,2976,4378,6432,9464,13913,20495,30205,44547,65670,96846,
%U A244459 142857,210941,311636,460613,680848,1006682,1488915,2203324,3261840,4830671
%N A244459 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5.
%H A244459 Alois P. Heinz, <a href="/A244459/b244459.txt">Table of n, a(n) for n = 6..900</a>
%p A244459 b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
%p A244459       1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244459       b(n-i*j, i-1, max(0,t-j), k), j=0..n/i)))
%p A244459     end:
%p A244459 a:= n-> b(n-1$2, 5$2) -b(n-1$2, 6$2):
%p A244459 seq(a(n), n=6..55);
%t A244459 b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 5, 5] - b[n - 1, n - 1, 6, 6]; Table[a[n], {n, 6, 55}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y A244459 Column k=5 of A244454.
%Y A244459 Cf. A244534.
%K A244459 nonn
%O A244459 6,7
%A A244459 _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014