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A069722
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Number of rooted unicursal planar maps with n edges and exactly one vertex of valency 1 (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path).
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4
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0, 4, 24, 160, 1120, 8064, 59136, 439296, 3294720, 24893440, 189190144, 1444724736, 11076222976, 85201715200, 657270374400, 5082890895360, 39392404439040, 305870434467840, 2378992268083200, 18531097667174400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..200
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FORMULA
| a(n)=2^(n-1)*binomial(2n-2, n-1), n>1
G.f. for a(n)^2: 1/AGM(1, (1-64*x)^(1/2)) Benoit Cloitre, Jan 01, 2004
a(n)=A059304(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2008]
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MAPLE
| Z:=(1-sqrt(1-z))*8^n/sqrt(1-z): Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2007
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MATHEMATICA
| Join[{0}, Table[2^(n-1) Binomial[2n-2, n-1], {n, 2, 20}]] (* From Harvey P. Dale, Nov 16 2011 *)
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PROG
| (MAGMA) [0] cat[2^(n-1)*Binomial(2*n-2, n-1): n in [2..20]]; // Vincenzo Librandi, Nov 17 2011
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CROSSREFS
| a(n)=2*A069723(n), n>1.
Cf. A069720, A069721, A089156.
Sequence in context: A117337 A084130 A059304 * A027079 A188913 A052685
Adjacent sequences: A069719 A069720 A069721 * A069723 A069724 A069725
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KEYWORD
| easy,nonn
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AUTHOR
| Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002
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