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Search: id:A069723
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| A069723 |
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a(1) = 1; for n > 1, a(n)=2^(n-2)*binomial(2n-2,n-1). |
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+0
17
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| 1, 2, 12, 80, 560, 4032, 29568, 219648, 1647360, 12446720, 94595072, 722362368, 5538111488, 42600857600, 328635187200, 2541445447680, 19696202219520, 152935217233920, 1189496134041600, 9265548833587200, 72271280901980160
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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 and two vertices of valency 1 (unicursal means that exactly two vertices 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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G.f. : 4x/(sqrt(1-8x)(1-sqrt(1-8x))). - Paul Barry (pbarry(AT)wit.ie), Sep 06 2004
a(n)=(0^n+2^n*binomial(2n, n))/2 [offset 0]. - Paul Barry (pbarry(AT)wit.ie), Sep 24 2004
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MAPLE
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Z:=(1-sqrt(1-z))*8^n/sqrt(1-z)/2: Zser:=series(Z, z=0, 33): seq(coeff(Zser, z, n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 16 2007
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CROSSREFS
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Main diagonal of array A082137.
a(n)=A069722(n)/2, n>1. Cf. A069720, A069721, A082143, A082144, A082145.
Cf. A088218.
Adjacent sequences: A069720 A069721 A069722 this_sequence A069724 A069725 A069726
Sequence in context: A062871 A107632 A082142 this_sequence A063481 A052822 A058872
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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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