OFFSET
0,9
COMMENTS
Also McKay-Thompson series of class 93B for Monster. - Michel Marcus, Feb 19 2014
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..2500 from G. C. Greubel)
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of G(q^31)*H(q) - q^6*H(q^31)*G(q) in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018
a(n) ~ exp(4*Pi*sqrt(n/93)) / (sqrt(2) * 93^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T93A = 1/q +q^5 +q^8 +q^11 +q^14 +q^17 +q^20 +2*q^23 +2*q^26 +...
MATHEMATICA
QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; B:= G[x^31]*H[x] - x^6*H[x^31]*G[x]; a:= CoefficientList[Series[B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Aug 28 2005
STATUS
approved