OFFSET
-1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = -1..1000
M. Koike, Mathieu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
FORMULA
Associated with permutations in Mathieu group M24 of shape (8)^2(4)(2)(1)^2.
G.f. is Fourier series of a level 8 modular function. f(-1/ (8 t)) = f(t) where q = exp(2 Pi i t).
a(n) ~ exp(sqrt(2*n)*Pi) / (2^(5/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
Expansion of -6 + (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^8 in powers of q. - G. C. Greubel, Jun 20 2018
EXAMPLE
1/q + 2 + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...
MATHEMATICA
QP = QPochhammer; s = -6*q + (QP[q^2]^8*QP[q^4]^8)/(QP[q]^8*QP[q^8]^8) + O[q]^30; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from PARI *)
PROG
(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); polcoeff( -6 + ( eta(x^2 + A) * eta(x^4 + A) / eta(x + A) / eta(x^8 + A) )^8 / x, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 22 2007
STATUS
approved
