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A098692
Main diagonal of array in A098691.
2
1, 2, 10, 78, 777, 9800, 149796, 2690420, 55555500, 1296871224, 33773107758, 970753545580, 30527491279005, 1042604500906800, 38430716820193144, 1520662246114589640, 64291516462902839175, 2892426397164199846860, 137970526315789473684210, 6955460736173788715925048, 369510689788116404049535299
OFFSET
1,2
COMMENTS
a(n) is the number of self-complementary n-bead primitive necklaces of n+1 colors (see Miller (1978)). - Petros Hadjicostas, Aug 21 2019
LINKS
H. Meyn and W. Götz, Self-reciprocal polynomials over finite fields, Séminaire Lotharingien de Combinatoire, B21d (1989), 8 pp.
R. L. Miller, Necklaces, symmetries and self-reciprocal polynomials, Discr. Math. 22 (1978), 25-33.
FORMULA
a(n) = ((n + 1)^n - 1)/(2*n) if n = 2^s (for s >= 1), and (1/(2*n)) * Sum_{d|n, d odd} mu(d) * (n + 1)^(n/d) otherwise. - Petros Hadjicostas, Aug 21 2019
MAPLE
with(numtheory):
a:= n-> `if`(n=2^ilog2(n) and n>1, (n+1)^n-1, add(mobius(d)*
(n+1)^(n/d), d=select(x-> x::odd, divisors(n))))/(2*n):
seq(a(n), n=1..20); # Alois P. Heinz, Aug 21 2019
CROSSREFS
Cf. A098691.
Sequence in context: A240599 A367142 A212381 * A300994 A307722 A138273
KEYWORD
nonn
AUTHOR
Ralf Stephan, Sep 21 2004
EXTENSIONS
More terms by Petros Hadjicostas, Aug 21 2019
STATUS
approved