OFFSET
1,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..500
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) = Sum_{k=1..n} k*A121685(n,k).
G.f.: (1 - 2*z) * (1 - 3*z - (1 - z)*sqrt(1 - 4*z))/(z^2*sqrt(1 - 4*z)).
Recurrence: (n + 2)*(n^2 - 2*n + 3)*a(n) = 2*(2*n - 1)*(n^2 + 2)*a(n-1). - Vaclav Kotesovec, Dec 10 2013
a(n) = 2*(n^2 + 2)*binomial(2*n, n)/((n + 1)*(n + 2)). - Vaclav Kotesovec, Dec 10 2013
EXAMPLE
a(1) = 2 because we have two binary trees with 1 edge, namely / and \, with a total of 2 branches.
MAPLE
G:=(1-2*z)*(1-3*z-(1-z)*sqrt(1-4*z))/z^2/sqrt(1-4*z): Gser:=series(G, z=0, 31): seq(coeff(Gser, z, n), n=1..27);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 15 2006
STATUS
approved