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Search: id:A006963
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| A006963 |
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Number of planar embedded labeled trees with n nodes: (2n-3)!/(n-1)!.
(Formerly M3076)
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+0
10
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| 1, 1, 3, 20, 210, 3024, 55440, 1235520, 32432400, 980179200, 33522128640, 1279935820800, 53970627110400, 2490952020480000, 124903451312640000, 6761440164390912000, 393008709555221760000, 24412776311194951680000, 1613955767240110694400000
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,'' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
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LINKS
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Index entries for sequences related to trees
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 109
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FORMULA
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E.g.f. for a(n+1), n >= 1, ln(c(x)); c(x) = g.f. for Catalan numbers A000108 - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*erfc(sqrt(x)/2)/2, x=0..infinity), n=0, 1..., where erfc(x) is the complementary error function. - Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 27 2001
a(n) ~ 2^(-5/2)*n^-2*2^(2*n)*e^-n*n^n - Joe Keane (jgk(AT)jgk.org), Jun 06 2002
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MAPLE
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a:=n->mul(j+add(1, j=0..n), j=1..n):seq(a(n), n=-1..18); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2008]
with(finance):seq(mul(cashflows([n, k, 1], 0), k=1..n), n=0..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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CROSSREFS
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Sequence in context: A052590 A081209 A014068 this_sequence A113333 A052851 A058477
Adjacent sequences: A006960 A006961 A006962 this_sequence A006964 A006965 A006966
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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