OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Valery A. Liskovets and Timothy 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
E.g.f.: x * (exp(4*x) * (BesselI(0,4*x) - BesselI(1,4*x)) - 1). - Ilya Gutkovskiy, Nov 03 2021
From Amiram Eldar, Jan 16 2024: (Start)
Sum_{n>=2} 1/a(n) = 1/7 + 8*arcsin(1/(2*sqrt(2)))/(7*sqrt(7)).
Sum_{n>=2} (-1)^n/a(n) = 1/9 + 4*log(2)/27. (End)
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
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Apr 07 2002
STATUS
approved