OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
FORMULA
a(n) = (n+3)*C(n+1) with C(n) the Catalan numbers A000108.
G.f.: c(x)*(4 - c(x))/sqrt(1 - 4*x) with c(x) the g.f. for the Catalan numbers.
From Amiram Eldar, May 16 2022: (Start)
Sum_{n>=0} 1/a(n) = 41/6 - 64*Pi/(9*sqrt(3)) + 2*Pi^2/3.
Sum_{n>=0} (-1)^n/a(n) = 57/10 - 256*log(phi)/(5*sqrt(5)) + 24*log(phi)^2, where phi is the golden ratio (A001622). (End)
MAPLE
seq((n+3)*binomial(2*n+2, n+1)/(n+2), n=0..24); # Zerinvary Lajos, Dec 08 2008
MATHEMATICA
Table[(n + 3) (CatalanNumber[n + 1]), {n, 0, 30}] (* Vincenzo Librandi, Sep 11 2016 *)
PROG
(Magma) [(n+3)*Catalan(n+1): n in [0..30]]; // Vincenzo Librandi, Sep 11 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved