OFFSET
1,2
REFERENCES
J. W. L. Glaisher, "On the Coefficients in the q-series for pi/2K and 2G/pi", Quart J. Pure and Applied Math., 21 (1885), 60-76.
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
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
Expansion of (eta(q^2)^2 / eta(q)^4 - 1) / 4 in powers of q.
a(n) = A001934(n) / 4.
EXAMPLE
q + 3*q^2 + 8*q^3 + 19*q^4 + 42*q^5 + 88*q^6 + 176*q^7 + 339*q^8 + 633*q^9 + ...
MAPLE
seq(coeff(convert(series(mul(( 1 - x^k )^(-(2+(k mod 2)*2)), k=1..100), x, 100), polynom), x, i)/4, i=1..50); (Pab Ter)
MATHEMATICA
Rest[CoefficientList[ Series[(1/EllipticTheta[4, 0, q]^2 - 1)/4, {q, 0, 34}], q]] (* Jean-François Alcover, Jul 18 2011 *)
a[ n_] := With[ {m = InverseEllipticNomeQ @ q}, SeriesCoefficient[ Integrate[ (EllipticK[m] - EllipticE[m]) / (8 Sqrt[1 - m] (Pi/2) q), q], {q, 0, n}]] (* Michael Somos, Jan 24 2012 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 / eta(x + A)^4 - 1, n) / 4)} /* Michael Somos, Feb 09 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 18 2005
STATUS
approved