OFFSET
-1,5
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..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).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of -1 + A*B/x in powers of q, where A = G(x^54)*G(x) + x^11* H(x^54)*H(x), B = G(x^27)*H(x^2) - x^5*H(x^27)*G(x^2), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018
a(n) ~ exp(2*Pi*sqrt(2*n/3)/3) / (6^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T54A = 1/q + q + q^2 + 3*q^3 + 2*q^4 + 4*q^5 + 3*q^6 + 6*q^7 + 5*q^8 + 9*q^9 + ...
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]; A:= G[x^54]*G[x^1] + x^11*H[x^54]*H[x^1]; B:= G[x^27]*H[x^2] - x^5*H[x^27]*G[x^2]; a:= CoefficientList[Series[-x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 24 2014
STATUS
approved