OFFSET
0,3
COMMENTS
Turning over is not allowed.
See A132100 for definition and comments.
Even and odd terms can be computed with the help of Burnside Lemma and recursive sequences. - Lionel RAVEL, Sep 18 2013
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
a(n) = (1/n)*Sum_{d|n} phi(d)*alpha(d, n/d), where phi = Euler's totient function,
alpha(p,q) = Sum_{j=0..q} p^j * binomial(2q, 2j) * (2j-1)!! if p even,
= p^q * (2q-1)!! if p odd. (cf. also A132100) - Laurent Tournier, Jul 09 2014
MAPLE
with(numtheory): a:=(p, q)->piecewise(p mod 2 = 1, p^q*doublefactorial(2*q - 1), sum(p^j*binomial(2*q, 2*j)*doublefactorial(2*j - 1), j = 0 .. q));
A132102 := n->add(phi(p)*a(p, n/p), p in divisors(n))/n;
[seq(A132102(n), n=1..20)]; # Laurent Tournier, Jul 09 2014
PROG
(PARI) a(n)={if(n<1, n==0, sumdiv(n, d, my(m=n/d); eulerphi(d)*sum(j=0, m, (d%2==0 || m-j==0) * binomial(2*m, 2*j) * d^j * (2*j)! / (j!*2^j) ))/n)} \\ Andrew Howroyd, Jan 26 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Keith F. Lynch, Oct 31 2007
EXTENSIONS
More terms from Lionel RAVEL, Sep 18 2013
a(9) and a(10) corrected, and addition of more terms using formula given above by Laurent Tournier, Jul 09 2014
STATUS
approved