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Search: id:A069731
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| A069731 |
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Number of unicursal planar maps with n edges rooted at a vertex of odd valency (unicursal means that exactly two vertices are of odd valency; there is an Eulerian path). |
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+0
1
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| 1, 5, 28, 168, 1056, 6864, 45760, 311168, 2149888, 15049216, 106502144, 760729600, 5477253120, 39710085120, 289650032640, 2124100239360, 15651264921600, 115819360419840, 860372391690240
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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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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FORMULA
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a(n)=2^(n-2)*C_(n+1), where C_n stands for the Catalan numbers (A000108).
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MAPLE
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Z:=-(1-4*z-sqrt(1-4*z))/sqrt(1-4*z)/64: Zser:=series(Z, z=0, 32): seq(coeff(Zser*2^(n+1), z, n), n=3..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2007
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CROSSREFS
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a(n)=A003645(n+2)/4
Cf. A069724, A069720, A000108, A003645.
Adjacent sequences: A069728 A069729 A069730 this_sequence A069732 A069733 A069734
Sequence in context: A025174 A083316 A027284 this_sequence A082031 A020081 A095676
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KEYWORD
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easy,nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002
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