OFFSET
0,2
COMMENTS
The q-series f_{32|8} is the g.f. for A082303. This is given on page 274 of McKay and Sebbar along with equation (8.1) which gives an expression for the g.f. A(q) of this sequence. - Michael Somos, Aug 15 2014
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.
FORMULA
Expansion of (21 * E_4(-q) - 16 * E_4(q^2)) / 5 in powers of q. [McKay and Sebbar, equation (8.1)] - Michael Somos, Aug 15 2014
G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = 16 (t/i)^4 f(t) where q = exp(2 Pi i t). - Michael Somos, Aug 15 2014
EXAMPLE
G.f. = 1 - 1008*x + 8304*x^2 - 28224*x^3 + 66672*x^4 - 127008*x^5 + 232512*x^6 + ...
G.f. = 1 - 1008*q^8 + 8304*q^16 - 28224*q^24 + 66672*q^32 - 127008*q^40 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; E4[0] := 1; E4[q_]:= 1 +240*Sum[k^3* q^k/(1 - q^k), {k, 1, 150}]; CoefficientList[Series[(21*E4[-q] - 16*E4[q^2])/5, {q, 0, 100}], q] (* G. C. Greubel, Jul 25 2018 *)
PROG
(Sage) A = ModularForms( Gamma0(8), 4, prec=32) . basis(); A[1] - 1008*A[2] + 8304*A[3] + 66672*A[4]; # Michael Somos, Aug 15 2014
CROSSREFS
KEYWORD
sign
AUTHOR
John McKay (mckay(AT)cs.concordia.ca), Apr 18 2004
EXTENSIONS
More terms from Michael Somos, Aug 15 2014
STATUS
approved