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Search: id:A069720
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| 1, 6, 40, 280, 2016, 14784, 109824, 823680, 6223360, 47297536, 361181184, 2769055744, 21300428800, 164317593600, 1270722723840, 9848101109760, 76467608616960, 594748067020800, 4632774416793600, 36135640450990080
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OFFSET
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1,2
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COMMENT
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Number of rooted unicursal planar maps with n edges (unicursal means that exactly two nodes are of odd valency; there is an Eulerian path).
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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)*binomial(2n, n)
G.f. : (1-sqrt(1-8x))/(4x*sqrt(1-8x))=2/(sqrt(1-8x)(1-sqrt(1-8x)))-1/(2x). - Paul Barry (pbarry(AT)wit.ie), Sep 06 2004
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MAPLE
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Z:=(1-sqrt(1-2*z))*4^(n-1)/sqrt(1-2*z): Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=1..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2007
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CROSSREFS
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First superdiagonal of number array A082137.
Cf. A069724, A003584, A069723, A082143.
Adjacent sequences: A069717 A069718 A069719 this_sequence A069721 A069722 A069723
Sequence in context: A083426 A122471 A090041 this_sequence A005037 A081337 A138240
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KEYWORD
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easy,nice,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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