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A244461 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 7.

%I A244461 #8 Feb 06 2015 09:14:50
%S A244461 1,0,0,0,0,0,0,1,2,2,2,2,2,2,4,7,12,16,21,25,30,38,52,74,108,151,206,
%T A244461 271,356,468,629,855,1180,1620,2212,2991,4030,5420,7320,9922,13508,
%U A244461 18396,25049,34032,46194,62653,85051,115548,157168,213852,291046,395990
%N A244461 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 7.
%H A244461 Alois P. Heinz, <a href="/A244461/b244461.txt">Table of n, a(n) for n = 8..900</a>
%p A244461 b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
%p A244461       1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244461       b(n-i*j, i-1, max(0,t-j), k), j=0..n/i)))
%p A244461     end:
%p A244461 a:= n-> b(n-1$2, 7$2) -b(n-1$2, 8$2):
%p A244461 seq(a(n), n=8..65);
%t A244461 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, 7, 7] - b[n - 1, n - 1, 8, 8]; Table[a[n], {n, 8, 65}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y A244461 Column k=7 of A244454.
%Y A244461 Cf. A244536.
%K A244461 nonn
%O A244461 8,9
%A A244461 _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014