OFFSET
-1,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
G.f.: u + v - 1 = u * v + 1 where u = Product_{k>0} (1 - x^k) * (1 - x^(15*k)) / ((1 - x^(6*k)) * (1 - x^(10*k))), v = 1/x * Product_{k>0} (1 - x^(3*k)) * (1 - x^(5*k)) / ((1 - x^(2*k)) * (1 - x^(30*k))). - Seiichi Manyama, May 04 2017
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jun 06 2018
Expansion of 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/(eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30)) in powers of q. - G. C. Greubel, Jun 14 2018
EXAMPLE
T30C = 1/q - 2*q^2 + 2*q^3 - 2*q^4 + 3*q^5 - 2*q^6 + 5*q^7 - 6*q^8 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(1 + eta[q]*eta[q^3]*eta[q^5]*eta[q^15]/(eta[q^2]*eta[q^6]* eta[q^10]* eta[q^30])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
QP=QPochhammer; a:= CoefficientList[Series[q + QP[q]*QP[q^3]*QP[q^5]* QP[q^15]/(QP[q^2]*QP[q^6]*QP[q^10]*QP[q^30]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
PROG
(PARI) q='q+O('q^50); A = 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/( eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30))/q; Vec(A) \\ G. C. Greubel, Jun 14 2018
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved