OFFSET
0,1
REFERENCES
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; Eq. (34.3).
FORMULA
Expansion of 2 * q^(-1/4) * (eta(q) * eta(q^4)^2 / eta(q^2)^3)^2 in powers of q. - Michael Somos, Jun 12 2012
a(n) ~ (-1)^n * exp(Pi*sqrt(n))/(2^(5/2)*n^(3/4)). - Vaclav Kotesovec, Jul 04 2016
2 * ({1} U (Euler transform of period 4 sequence [-2, 4, -2, 0])). - Georg Fischer, Dec 06 2022
EXAMPLE
2 - 4*x + 10*x^2 - 20*x^3 + 36*x^4 - 64*x^5 + 110*x^6 - 180*x^7 + 288*x^8 - ...
2*q^(1/4) - 4*q^(5/4) + 10*q^(9/4) - 20*q^(13/4) + 36*q^(17/4) - 64*q^(21/4) + ...
MATHEMATICA
QP = QPochhammer; s = 2*(QP[q]*(QP[q^4]^2/QP[q^2]^3))^2 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 27 2015, adapted from PARI *)
nmax = 50; CoefficientList[Series[2*Product[(1+x^(2*k))^4 / (1+x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 04 2016 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 2 * (eta(x + A) * eta(x^4 + A)^2 / eta(x^2 + A)^3)^2, n))} /* Michael Somos, Jun 12 2012 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Mar 31 2007
STATUS
approved