A034949 Expansion of eta(8z)*eta(16z)*theta_3(z).

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, -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, 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

Offset

1,2

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Matija Kazalicki, Congruent numbers and congruences between half-integral weight modular forms, Journal of Number Theory 133.4 (2013): 1079-1085; MR 3003987 [From N. J. A. Sloane, Oct 18 2014]

Formula

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

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

Example

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

Mathematica

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A258322 A258034 A243828 * A263767 A185338 A208603

Adjacent sequences: A034946 A034947 A034948 * A034950 A034951 A034952

Keyword

sign

Author

N. J. A. Sloane

Status

approved