OFFSET
0,6
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of f(-q) * psi(q^5) in powers of q where f(),psi() are Ramanujan theta functions.
Euler transform of period 10 sequence [ -1, -1, -1, -1, 0, -1, -1, -1, -1, -2, ...].
G.f.: Product_{k>0} (1-x^k)*(1-x^(5k))*(1+x^(5k))^2.
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-2/3)* eta[q]*eta[q^10]^2/eta[q^5], {q, 0, 50}], q] (* G. C. Greubel, Apr 17 2018 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^10+A)^2/eta(x^5+A), n))}
(PARI) q='q+O('q^99); Vec(eta(q)*eta(q^10)^2/eta(q^5)) \\ Altug Alkan, Apr 18 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Oct 13 2006; corrected Jul 29 2007
STATUS
approved