OFFSET
-1,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..5000
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 -1 + psi(q) / (q * psi(q^9)) + 3 * q * psi(q^9) / psi(q) in powers of q where psi() is a Ramanujan theta function. - Michael Somos, Aug 09 2012
a(n) = A123676(n) = A215412(n) = A215413(n) unless n=0. a(n) = -(-1)^n * A058644(n). - Michael Somos, Aug 09 2012
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
EXAMPLE
T18C = 1/q + 3*q - 2*q^2 + 3*q^3 - 6*q^4 + 10*q^5 - 12*q^6 + 15*q^7 - ...
MATHEMATICA
QP = QPochhammer; s = -q + QP[q^3]^6 / (QP[q]*QP[q^2]*QP[q^6]^2*QP[q^9]* QP[q^18]) + O[q]^50; CoefficientList[s, q] (* Jean-François Alcover, Nov 12 2015, adapted from PARI *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( -x + eta(x^3 + A)^6 / (eta(x + A) * eta(x^2 + A) * eta(x^6 + A)^2 * eta(x^9 + A) * eta(x^18 + A)), n))}; /* Michael Somos, Aug 09 2012 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved