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%I #9 Feb 06 2015 08:10:27
%S 1,0,0,0,0,0,1,2,2,2,2,2,4,7,12,16,21,25,34,47,70,103,147,201,276,377,
%T 527,743,1057,1486,2088,2911,4073,5704,8027,11290,15897,22340,31411,
%U 44159,62165,87516,123296,173642,244636,344684,485976,685362,966971,1364301
%N Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 6.
%H Alois P. Heinz, <a href="/A244460/b244460.txt">Table of n, a(n) for n = 7..900</a>
%p b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
%p 1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p b(n-i*j, i-1, max(0,t-j), k), j=0..n/i)))
%p end:
%p a:= n-> b(n-1$2, 6$2) -b(n-1$2, 7$2):
%p seq(a(n), n=7..60);
%t 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, 6, 6] - b[n - 1, n - 1, 7, 7]; Table[a[n], {n, 7, 60}] (* _Jean-François Alcover_, Feb 06 2015, after Maple *)
%Y Column k=6 of A244454.
%Y Cf. A244535.
%K nonn
%O 7,8
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 29 2014
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