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A244404
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Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 8.
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2
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1, 2, 6, 17, 50, 143, 416, 1199, 3473, 10042, 29089, 84259, 244316, 708679, 2057087, 5974077, 17359390, 50467157, 146789962, 427148444, 1243513350, 3621591235, 10551595959, 30753712080, 89666493709, 261522175986, 763002239120, 2226771020793, 6500575182332
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OFFSET
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9,2
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LINKS
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MAPLE
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b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 8$2) -`if`(k=0, 0, b(n-1$2, 7$2)):
seq(a(n), n=9..40);
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MATHEMATICA
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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, 8, 8] - If[n == 0, 0, b[n - 1, n - 1, 7, 7]]; Table[a[n], {n, 9, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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