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A244403
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Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 7.
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2
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1, 2, 6, 17, 50, 143, 416, 1198, 3467, 10019, 29001, 83945, 243228, 705012, 2044935, 5934425, 17231410, 50058023, 145491836, 423056364, 1230683672, 3581556220, 10427172296, 30368394833, 88476965536, 257860132679, 751756288476, 2192311994070, 6395199688864
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OFFSET
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8,2
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LINKS
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FORMULA
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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, 7$2) -`if`(k=0, 0, b(n-1$2, 6$2)):
seq(a(n), n=8..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, 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 *)
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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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