OFFSET
0,4
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} mu(n/d)*binomial(4*d, d)) - 3*binomial(4*n, n)/(3*n+1) for n > 0. - Andrew Howroyd, Apr 30 2018
MATHEMATICA
a[0] = 1;
a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[4#, #]&]/n - 3 Binomial[4n, n]/(3n + 1);
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 29 2018, after Andrew Howroyd *)
PROG
(PARI) a(n) = if(n==0, 1, sumdiv(n, d, moebius(n/d)*binomial(4*d, d))/n - 3*binomial(4*n, n)/(3*n+1)) \\ Andrew Howroyd, Apr 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(13) and beyond from Andrew Howroyd, May 02 2018
STATUS
approved