OFFSET
-1,9
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 + (1/q) * chi(-q) * chi(-q^23) in powers of q where chi() is a Ramanujan theta function. - Michael Somos, Jun 07 2006
G.f.: 1 + (1/x) * Product_{k>0} 1 / ((1 + x^k) * (1 + x^(23*k))).
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v^2 - v + 2 - 2*u + u^2 - v*u^2. - Michael Somos, Feb 14 2007
a(n) = A132322(n) unless n=0.
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/23)) / (2 * 23^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 06 2018
Expansion of 1 + eta(q)*eta(q^23)/(eta(q^2)*eta(q^46)) in powers of q. - G. C. Greubel, Jun 16 2018
EXAMPLE
T46A = 1/q - q^2 + q^3 - q^4 + q^5 - q^6 + 2*q^7 - 2*q^8 + 2*q^9 + ...
MATHEMATICA
QP = QPochhammer; s = q + QP[q]*(QP[q^23]/(QP[q^2]*QP[q^46])) + O[q]^70; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(1+eta[q] *eta[q^23]/(eta[q^2]*eta[q^46])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( x + eta(x + A) * eta(x^23 + A) / (eta(x^2 + A) * eta(x^46 + A)), n))} /* Michael Somos, Feb 14 2007 */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
STATUS
approved