OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..3239
FORMULA
EXAMPLE
H_1 = 1/10 = 1/2 - 2/5 = 1/10, so a(1) = 1.
H_2 = 3/10 = 1/2 + 2^2/5 - 1 = 13/10 - 1, so a(2) = 13.
H_3 = 567/130 = 1/2 - 2^3/5 + 6/13 + 5 = -83/130 + 5, so a(3) = -83.
H_4 = 43659/170 = 1/2 + 2^4/5 + 2/17 + 253 = 649/170 + 253, so a(4) = 649.
MATHEMATICA
nmax = 28; H[n_] := (n*(4*n - 2)!/(2^(4*n - 2)))*SeriesCoefficient[ WeierstrassP[z, {4, 0}], {z, 0, 4*n - 2}]; pp = Select[Prime[Range[2 nmax]], Mod[#, 4] == 1 &]; Scan[(chi[#] = -Sum[JacobiSymbol[x^3 - x, #], {x, 0, # - 1}])&, pp]; a[n_] := 1/2 + Sum[If[Divisible[4 n, p - 1], chi[p]^(4*n/(p - 1))/p, 0], {p, pp}] // Numerator; Array[a, nmax] (* Jean-François Alcover, Oct 22 2016 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 26 2016
STATUS
approved