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A060279 Number of labeled rooted trees with all 2n nodes of odd degree. 1
2, 16, 576, 47104, 6860800, 1562148864, 512260833280, 228646878969856, 133296779352342528, 98349146136012390400, 89583293999931442855936, 98732413018143104723582976, 129497500112719525122855141376, 199333356644821012200519079297024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
There are no such trees with an odd number of nodes.
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
LINKS
FORMULA
a(n) = (n/2^n)*Sum_{k=0..n} binomial(n, k)*(n-2*k)^(n-2).
a(n) = 2*n * A007106(n).
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
MAPLE
a:= j-> (n-> (n/2^n)*add(binomial(n, k)*(n-2*k)^(n-2), k=0..n))(2*j):
seq(a(n), n=1..15); # Alois P. Heinz, Sep 27 2020
MATHEMATICA
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 *)
PROG
(PARI) a(n) = n/2^n*sum(k=0, n, binomial(n, k)*(n-2*k)^(n-2)) \\ Michel Marcus, Jun 17 2013
CROSSREFS
Cf. A007106.
Sequence in context: A012679 A012726 A013177 * A369674 A012757 A012464
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 28 2001
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)