OFFSET
-1,3
COMMENTS
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, Commun. Algebra 22, No. 13, 5175-5193 (1994).
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^-1 * (chi(-q) * chi(-q^5))^4 + 4 in powers of q where chi() is a Ramanujan theta function.
Expansion of (eta(q) * eta(q^5) / (eta(q^2) * eta(q^10)))^4 + 4 in powers of q.
G.f.: (Product_{k>0} (1 + x^k) * (1 + x^(5*k)))^-4 + 4.
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
EXAMPLE
T10B = 1/q + 6*q - 8*q^2 + 17*q^3 - 32*q^4 + 54*q^5 - 80*q^6 + ...
MATHEMATICA
QP = QPochhammer; s = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, n))} /* Michael Somos, Feb 02 2012 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved