OFFSET
0,2
COMMENTS
Convolution square is A328785. - Michael Somos, Nov 02 2019
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1260
FORMULA
a(n) ~ (-1)^n * c * exp(Pi*n/sqrt(3)), where c = A258942 = 8*exp(Pi/(6*sqrt(3))) * Pi^(5/2) / Gamma(1/6)^3 = 1.09786330972731096865822482325074133091288... . - Vaclav Kotesovec, Nov 14 2015
Expansion of q^(-1/6)* eta[q]*eta[q^9]^2/(eta[q]^3 + 9*eta[q^9]^3) in powers of q. - G. C. Greubel, Jun 22 2018
Expansion of q^(-1/6) * 3^(-1/2) * sqrt(b(q)*c(q))/a(q) in powers of q where a(), b(), c() are cubic AGM functions. - Michael Somos, Nov 02 2019
EXAMPLE
G.f. = 1 - 7*x + 41*x^2 - 253*x^3 + 1555*x^4 - 9532*x^5 + ... - Michael Somos, Nov 02 2019
G.f. = q - 7*q^7 + 41*q^13 - 253*q^19 + 1555*q^25 - 9532*q^31 + ... - Michael Somos, Nov 02 2019
MATHEMATICA
CoefficientList[Series[QPochhammer[x, x] * QPochhammer[x^3, x^3]^2 / (QPochhammer[x, x]^3 + 9*x*QPochhammer[x^9, x^9]^3), {x, 0, 50}], x]
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/6)* eta[q]*eta[q^9]^2/(eta[q]^3 + 9*eta[q^9]^3), {q, 0, 60}], q] (* G. C. Greubel, Jun 22 2018 *)
a[ n_] := SeriesCoefficient[ QPochhammer[x] QPochhammer[x^3]^2 / (QPochhammer[x]^3 + 9 x QPochhammer[x^9]^3), {x, 0, n}]; (* Michael Somos, Nov 02 2019 *)
PROG
(PARI) q='q+O('q^50); A = eta(q)*eta(q^3)^2/(eta(q)^3 + 9*q*eta(q^9)^3); Vec(A) \\ G. C. Greubel, Jun 22 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Nov 07 2015
STATUS
approved