OFFSET
1,2
COMMENTS
Number of certain rooted planar maps.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Daniel Birmajer, Juan B. Gil, Michael D. Weiner, Bounce statistics for rational lattice paths, arXiv:1707.09918 [math.CO], 2017, p. 10.
W. G. Brown, Enumeration of non-separable planar maps, Canad. J. Math., 15 (1963), 526-545.
W. G. Brown, Enumeration of non-separable planar maps [Annotated scanned copy]
FORMULA
From Emeric Deutsch, Mar 03 2004: (Start)
a(n) = 2*binomial(3*n-3, n-1)/(2*n-1) for n >= 2, and a(1) = 1.
a(n) = 2*A001764(n-1) for n >= 2. (End)
a(n) = (n+1) * A000139(n). - F. Chapoton, Feb 23 2024
G.f.: (1+g)/(1-g) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
MAPLE
alias(PS=ListTools:-PartialSums): A046646List := proc(m) local A, P, n;
A := [1, 2]; P := [2]; for n from 1 to m - 2 do P := PS(PS([op(P), P[-1]]));
A := [op(A), P[-1]] od; A end: A046646List(22); # Peter Luschny, Mar 26 2022
MATHEMATICA
Join[{1}, Table[(2*Binomial[3n-3, n-1])/(2n-1), {n, 2, 30}]] (* Harvey P. Dale, Oct 12 2013 *)
PROG
(Magma) [1] cat [2*Binomial(3*n-3, n-1)/(2*n-1): n in [2..30]]; // Vincenzo Librandi, Oct 13 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Mar 03 2004
New name using a formula of Emeric Deutsch by Peter Luschny, Feb 23 2024
STATUS
approved