OFFSET
0,2
COMMENTS
The convolution square of this sequence is A107080, except for the constant term. - G. A. Edgar, Mar 22 2017
LINKS
G. A. Edgar, Table of n, a(n) for n = 0..999
D. Alexander, C. Cummins, J. McKay and C. Simons, Completely Replicable Functions, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of q^(1/2) * (eta(q)^4 / eta(q^4)^4 - 4^2*eta(q^4)^4 / eta(q)^4) in powers of q. - G. A. Edgar, Mar 22 2017
a(n) ~ -exp(sqrt(2*n)*Pi) / (2^(5/4)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
EXAMPLE
T8a = 1/q - 20*q - 62*q^3 - 216*q^5 - 641*q^7 - 1636*q^9 - 3778*q^11 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 - x^k)^4/(1 - x^(4*k))^4, {k, 1, nmax}] - 16*x*Product[(1 - x^(4*k))^4/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]/eta[q^4])^4; a:= CoefficientList[Series[A - 16*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)
PROG
(PARI) q='q+O('q^66); Vec((eta(q)^4 / eta(q^4)^4 - q*4^2*eta(q^4)^4 / eta(q)^4)) \\ Joerg Arndt, Mar 23 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Aug 28 2005
EXTENSIONS
More terms from G. A. Edgar, Mar 23 2017
STATUS
approved