OFFSET
-1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..5000 (terms -1..997 from G. A. Edgar)
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
G.f. is a period 1 Fourier series which satisfies f(-1 / (81 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Aug 28 2015
Expansion of A - 3/A, where A = (eta(q^9)^2/(eta(q^3)*eta(q^27)))^2, in powers of q. - G. C. Greubel, Jun 03 2018
EXAMPLE
T9d = 1/q - 3*q + 2*q^2 + 6*q^4 + 5*q^5 + 3*q^7 + 6*q^8 - 18*q^10 + 12*q^11 + ...
MATHEMATICA
a[ n_] := With[ {A = 1/q (QPochhammer[ q^9]^2 / (QPochhammer[ q^3] QPochhammer[ q^27]))^2}, seriesCoefficient[ A - 3 / A, {q, 0, n}]]; (* Michael Somos, Aug 28 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A := (eta[q^9]^2/(eta[q^3]*eta[q^27]) )^2; a := CoefficientList[Series[q*(A - 3/A), {q, 0, 60}], q];
Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 03 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = eta(x^9 + A)^4 / (eta(x^3 + A) * eta(x^27 + A))^2; polcoeff( A - 3 * x^2 / A, n))}; /* Michael Somos, Aug 28 2015 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved