OFFSET
0,2
COMMENTS
a(n) is also the number of ways of returning to an empty table for the first time after exactly 2n + 2 steps in the game of plates and olives. See the Carroll & Galvin link for a description of the game of plates and olives.
REFERENCES
L. Nicolaescu, Counting Morse functions on the 2-sphere, Compositio Math. 144.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
Teena Carroll, David Galvin, The game of plates and olives, arXiv:1711.10670 [math.CO], 2017.
Andrew Howroyd, PARI Code
L. Nicolaescu, Counting Morse functions on the 2-sphere, Compositio Math. 144 (2008).
FORMULA
a(n) >= A001147(n) = (2*n - 1)!!. - David A. Corneth, Nov 30 2017
EXAMPLE
From David A. Corneth, Nov 30 2017: (Start)
a(0) = 1 as there is exactly one way to get an empty table for the first time in two steps:
Step 1: an empty plate is placed on the table.
Step 2: an empty plate is removed from the table. (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 30 2017
EXTENSIONS
a(6)-a(18) from Kyle Weingartner, Dec 04 2017
New name from Kyle Weingartner, Dec 05 2017
STATUS
approved