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A069722 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). 4
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; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

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-1)*binomial(2n-2, n-1), n>1.

a(n) = 2*A069723(n), 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. [R. J. Mathar, Sep 29 2008]

a(n) ~ 2^(3*n-3)/sqrt(Pi*n). - Vaclav Kotesovec, Sep 28 2019

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, Jan 01 2007

MATHEMATICA

Join[{0}, Table[2^(n-1) Binomial[2n-2, n-1], {n, 2, 20}]] (* Harvey P. Dale, Nov 16 2011 *)

PROG

(MAGMA) [0] cat[2^(n-1)*Binomial(2*n-2, n-1): n in [2..20]]; // Vincenzo Librandi, Nov 17 2011

CROSSREFS

Cf. A069720, A069721, A069723, A089156.

Sequence in context: A272865 A084130 A059304 * A027079 A213441 A238299

Adjacent sequences:  A069719 A069720 A069721 * A069723 A069724 A069725

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Apr 07 2002

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)