OFFSET
2,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 2..152
L. Carlitz, The coefficients of the lemniscate function, Math. Comp., 16 (1962), 475-478.
A. Hurwitz, Über die Entwicklungskoeffizienten der lemniskatischen Funktionen, Math. Ann., 51 (1899), 196-226; Mathematische Werke. Vols. 1 and 2, Birkhäuser, Basel, 1962-1963, see Vol. 2, No. LXVII.
A. Hurwitz, Über die Entwicklungskoeffizienten der lemniskatischen Funktionen, Math. Ann., 51 (1899), 196-226; Mathematische Werke. Vols. 1 and 2, Birkhäuser, Basel, 1962-1963, see Vol. 2, No. LXVII. [Annotated scanned copy]
FORMULA
a(n) = A002306(n) / A047817(n) - 1/2 - sum(chi(p)^(4*n / (p-1))/p) where the sum is over primes p of the form 4k+1 such that p-1 divides 4*n and the numbers chi(p) are given by A002172. The resulting a(n) is an integer despite all the rationals. - Sean A. Irvine, Aug 17 2014
MATHEMATICA
nmax = 20; 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_] := H[n] - 1/2 - Sum[If[Divisible[4 n, p - 1], chi[p]^(4*n/(p - 1))/p, 0], {p, pp}]; Table[a[n], {n, 2, nmax}] (* Jean-François Alcover, Dec 11 2014, updated Oct 22 2016 *)
CROSSREFS
KEYWORD
sign,easy,nice
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 07 2004
STATUS
approved
