A058704 McKay-Thompson series of class 51A for the Monster group.

1, 0, 1, 2, 2, 2, 5, 4, 6, 8, 9, 10, 17, 16, 19, 26, 29, 34, 46, 48, 59, 72, 80, 92, 117, 126, 148, 178, 198, 226, 274, 298, 345, 404, 450, 510, 601, 660, 753, 866, 965, 1084, 1253, 1378, 1558, 1770, 1965, 2196, 2501, 2752, 3085, 3476, 3845, 4276, 4820, 5298

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

Index entries for McKay-Thompson series for Monster simple group

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

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A346500 A103286 A285704 * A316660 A098101 A257670

Adjacent sequences: A058701 A058702 A058703 * A058705 A058706 A058707

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved