%I #21 Nov 06 2017 02:43:27

%S 1,2,0,0,2,0,0,0,-1,0,0,0,-2,0,0,0,0,-6,0,0,-4,0,0,0,-1,0,0,0,2,0,0,0,

%T -4,0,0,0,2,0,0,0,4,0,0,0,2,0,0,0,1,10,0,0,-2,0,0,0,4,0,0,0,2,0,0,0,4,

%U 0,0,0,0,0,0,0,-4,0,0,0,0,0,0,0,-3,0,0,0,4,0,0,0,-4,0,0,0,-4,0,0,0,0

%N Expansion of eta(8z)*eta(16z)*theta_3(z).

%D Ono and Skinner, Ann. Math., 147 (1998), 453-470.

%H G. C. Greubel, <a href="/A034949/b034949.txt">Table of n, a(n) for n = 1..1000</a>

%H Matija Kazalicki, <a href="http://dx.doi.org/10.1016/j.jnt.2012.09.018">Congruent numbers and congruences between half-integral weight modular forms</a>, Journal of Number Theory 133.4 (2013): 1079-1085; MR 3003987 [From _N. J. A. Sloane_, Oct 18 2014]

%F Expansion of eta(q^2)^5 * eta(q^8) * eta(q^16) / (eta(q)^2 * eta(q^4)^2) in powers of q. - _Michael Somos_, Nov 03 2011

%F Euler transform of period 16 sequence [ 2, -3, 2, -1, 2, -3, 2, -2, 2, -3, 2, -1, 2, -3, 2, -3, ...]. - _Michael Somos_, Nov 03 2011

%e x + 2*x^2 + 2*x^5 - x^9 - 2*x^13 - 6*x^18 - 4*x^21 - x^25 + 2*x^29 + ...

%t QP = QPochhammer; s = QP[q^2]^5*QP[q^8]*(QP[q^16]/(QP[q]^2*QP[q^4]^2)) + O[q]^100; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 25 2015, after _Michael Somos_ *)

%o (PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^8 + A) * eta(x^16 + A) / (eta(x + A)^2 * eta(x^4 + A)^2), n))} /* _Michael Somos_, Nov 03 2011 */

%K sign

%O 1,2

%A _N. J. A. Sloane_