%I #24 Nov 29 2015 05:08:43
%S 0,0,0,1,-2,0,0,-16,36,0,0,99,-272,0,0,-240,1056,0,0,-253,-1800,0,0,
%T 2736,-1464,0,0,-4284,12544,0,0,-6816,-19008,0,0,27270,-4554,0,0,
%U -6864,39880,0,0,-66013,-26928,0,0,44064,12544,0,0
%N Coefficients of Jacobi cusp form of index 1 and weight 10.
%D M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 141.
%F Expansion of eta(4z)^18 * theta_4(z) or (theta_2(z)^12 * theta_3(z)^3 * theta_4(z)^4) / 4096. - Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 11 2000
%F Euler transform of period 4 sequence [ -2, -1, -2, -19, ...]. - _Michael Somos_, Mar 20 2004
%F Expansion of eta(q)^2 * eta(q^4)^18 / eta(q^2) in powers of q. - _Michael Somos_, Mar 20 2004
%F G.f.: x^3 * (Product_{k>0} (1 - x^k) * (1 - x^(4*k))^18 / (1 + x^k)). - _Michael Somos_, Mar 20 2004
%F a(4*n + 1) = a(4*n + 2) = 0.
%F G.f. for a(4*n + 3) = eta(q)^16 * eta(q^2)^5 / eta(q^4)^2; for a(4*n + 4) = -2 * eta(q)^18 * eta(q^4)^2 / eta(q^2). - _Michael Somos_, Mar 20 2004
%e q^3 - 2*q^4 - 16*q^7 + 36*q^8 + 99*q^11 - 272*q^12 - 240*q^15 + 1056*q^16 + ...
%t QP = QPochhammer; s = q^3*QP[q]^2*(QP[q^4]^18/QP[q^2]) + O[q]^60; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 29 2015, adapted from PARI *)
%o (PARI) {a(n) = local(A); if( n<3, 0, n-=3; A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^4 + A)^18 / eta(x^2 + A), n))} /* _Michael Somos_, Mar 20 2004 */
%Y Cf. A003785.
%K sign
%O 0,5
%A _N. J. A. Sloane_