OFFSET
0,5
REFERENCES
M. Eichler and D. Zagier, The Theory of Jacobi Forms, Birkhauser, 1985, p. 141.
FORMULA
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
Euler transform of period 4 sequence [ -2, -1, -2, -19, ...]. - Michael Somos, Mar 20 2004
Expansion of eta(q)^2 * eta(q^4)^18 / eta(q^2) in powers of q. - Michael Somos, Mar 20 2004
G.f.: x^3 * (Product_{k>0} (1 - x^k) * (1 - x^(4*k))^18 / (1 + x^k)). - Michael Somos, Mar 20 2004
a(4*n + 1) = a(4*n + 2) = 0.
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
EXAMPLE
q^3 - 2*q^4 - 16*q^7 + 36*q^8 + 99*q^11 - 272*q^12 - 240*q^15 + 1056*q^16 + ...
MATHEMATICA
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 *)
PROG
(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 */
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved