|
| |
|
|
A069720
|
|
a(n)=2^(n-1)C(2n-1,n)
|
|
18
| |
|
|
1, 6, 40, 280, 2016, 14784, 109824, 823680, 6223360, 47297536, 361181184, 2769055744, 21300428800, 164317593600, 1270722723840, 9848101109760, 76467608616960, 594748067020800, 4632774416793600, 36135640450990080
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Number of rooted unicursal planar maps with n edges (unicursal means that exactly two nodes are of odd valency; there is an Eulerian path).
|
|
|
REFERENCES
| H. J. Brothers, Pascal's Prism: Supplementary Material, http://www.brotherstechnology.com/docs/Pascal's_Prism_(supplement).pdf.
V. A. Liskovets and T. R. S. Walsh, Enumeration of Eulerian and unicursal planar maps, Discr. Math., 282 (2004), 209-221.
|
|
|
FORMULA
| 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
|
|
|
MAPLE
| 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
|
|
|
CROSSREFS
| First superdiagonal of number array A082137.
Cf. A069724, A003584, A069723, A082143.
Sequence in context: A122471 A178397 A090041 * A005037 A081337 A138240
Adjacent sequences: A069717 A069718 A069719 * A069721 A069722 A069723
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| Valery A. Liskovets (liskov(AT)im.bas-net.by), Apr 07 2002
|
| |
|
|
