OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
Miklos Bona, Michel Bousquet, Gilbert Labelle, and Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56.
FORMULA
a(n) = (1/n)*(Sum_{d|n} phi(n/d)*binomial(3*d, d)) - 2*binomial(3*n, n)/(2*n+1) for n > 0. - Andrew Howroyd, May 02 2018
a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi) * 2^(2*n + 2) * n^(5/2)). - Vaclav Kotesovec, Jul 17 2017
MATHEMATICA
a[n_] := If[n == 0, 1, (Binomial[3*n, n]/(2*n+1) + DivisorSum[n, Binomial[ 3*#, #]*EulerPhi[n/#]*Boole[# < n]&])/n]; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Jul 17 2017 *)
PROG
(PARI) a(n) = if(n==0, 1, sumdiv(n, d, eulerphi(n/d)*binomial(3*d, d))/n - 2*binomial(3*n, n)/(2*n+1)) \\ Andrew Howroyd, May 02 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Jean-François Alcover, Jul 17 2017
STATUS
approved