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A244403 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 7.

%I A244403 #9 Feb 09 2015 11:03:26
%S A244403 1,2,6,17,50,143,416,1198,3467,10019,29001,83945,243228,705012,
%T A244403 2044935,5934425,17231410,50058023,145491836,423056364,1230683672,
%U A244403 3581556220,10427172296,30368394833,88476965536,257860132679,751756288476,2192311994070,6395199688864
%N A244403 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 7.
%H A244403 Alois P. Heinz, <a href="/A244403/b244403.txt">Table of n, a(n) for n = 8..1000</a>
%F A244403 a(n) = A182378(n) - A036722(n).
%p A244403 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244403       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244403        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244403     end:
%p A244403 a:= n-> b(n-1$2, 7$2) -`if`(k=0, 0, b(n-1$2, 6$2)):
%p A244403 seq(a(n), n=8..40);
%t A244403 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, 7, 7] - If[n == 0, 0, b[n - 1, n - 1, 6, 6]]; Table[a[n], {n, 8, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)
%Y A244403 Column k=7 of A244372.
%Y A244403 Cf. A036722, A182378.
%K A244403 nonn
%O A244403 8,2
%A A244403 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014