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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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15
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| For n>1: central terms of the triangle in A173333; cf. A001761, A001813. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 19 2010]
Can be obtained from the Vandermonde permanent of the first n positive integers; see A203468. [From Clark Kimberling, Jan 02 2012]
E.g.f. (A(x)-1) is reversion of F(x)=exp(-x)-exp(-2*x). [From Vladimir Kruchinin, Jan 30 2012]
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 109
Index entries for sequences related to trees
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FORMULA
| 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
a(n+1) = (n+1)*(n+2)*...*(2n-1) for n>=2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 09 2010]
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MATHEMATICA
| Join[{1}, Table[(2n-3)!/(n-1)!, {n, 2, 20}]] (* From Harvey P. Dale, Nov 03 2011 *)
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PROG
| (MAGMA) [1] cat [Factorial(2*n-3)/Factorial(n-1): n in [2..20]]; // Vincenzo Librandi, Nov 12 2011
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CROSSREFS
| Cf. A203468.
Sequence in context: A081209 A196560 A014068 * A113333 A206405 A052851
Adjacent sequences: A006960 A006961 A006962 * A006964 A006965 A006966
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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