OFFSET
-1,3
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, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of sqrt( 4 + (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^4 ) in powers of q. - G. C. Greubel, Jun 14 2018
a(n) ~ -(-1)^n * exp(sqrt(2*n/5)*Pi) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T20d = 1/q + 3*q^3 - 4*q^5 + 4*q^7 - 4*q^9 + 7*q^11 - 12*q^13 + 13*q^15 - ...
MATHEMATICA
QP = QPochhammer; A = (QP[q]*(QP[q^5]/QP[q^2]/QP[q^10]))^4 + 4*q + O[q]^40;
CoefficientList[Sqrt[A], q] (* Georg Fischer, Nov 15 2020 *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff(sqrtn( (eta(x + A) * eta(x^5 + A) / eta(x^2 + A) / eta(x^10 + A))^4 + 4 * x, 2), n))} /* Georg Fischer, Nov 15 2020 [adapted from Michael Somos' PARI in A058098] */
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 14 2018
STATUS
approved