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A060279
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Number of labeled rooted trees with all 2n nodes of odd degree.
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1
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2, 16, 576, 47104, 6860800, 1562148864, 512260833280, 228646878969856, 133296779352342528, 98349146136012390400, 89583293999931442855936, 98732413018143104723582976, 129497500112719525122855141376, 199333356644821012200519079297024
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OFFSET
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1,1
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COMMENTS
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There are no such trees with an odd number of nodes.
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
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LINKS
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FORMULA
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a(n) = (n/2^n)*Sum_{k=0..n} binomial(n, k)*(n-2*k)^(n-2).
a(n) ~ sqrt(1+s^2) * s^(2*n-1) * 2^(2*n) * n^(2*n-1) / exp(2*n), where s = 1.5088795615383199289... is the root of the equation sqrt(1+s^2) = s*log(s+sqrt(1+s^2)). - Vaclav Kotesovec, Jan 23 2014
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MAPLE
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a:= j-> (n-> (n/2^n)*add(binomial(n, k)*(n-2*k)^(n-2), k=0..n))(2*j):
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MATHEMATICA
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Flatten[{2, Table[n/2^n*Sum[Binomial[n, k]*(n-2*k)^(n-2), {k, 0, n}], {n, 4, 30, 2}]}] (* Vaclav Kotesovec, Jan 23 2014 *)
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PROG
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(PARI) a(n) = n/2^n*sum(k=0, n, binomial(n, k)*(n-2*k)^(n-2)) \\ Michel Marcus, Jun 17 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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