OFFSET
-1,4
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 A*B in powers of q, where A = G(q^17)*G(q^3) + q^4*H(q^17) *H(q^3), B = G(q^51)*H(q) - q^10*H(q^51)*G(q), 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/51)) / (sqrt(2) * 51^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018
EXAMPLE
T51A = 1/q + q + 2*q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 6*q^7 + 8*q^8 + ...
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^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; a := CoefficientList[Series[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