A112210 McKay-Thompson series of class 82a for the Monster group.

1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 9, 9, 11, 12, 14, 15, 18, 19, 22, 24, 27, 29, 34, 36, 41, 44, 50, 54, 61, 65, 73, 79, 88, 95, 106, 114, 126, 136, 150, 162, 179, 192, 211, 228, 249, 268, 294, 316, 345, 371, 404, 434, 473, 507, 551, 592, 641, 688

Offset

-1,7

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of G(q^41)*H(q) - q^8*H(q^41)*G(q) in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(2*Pi*sqrt(2*n/41)) / (2^(3/4) * 41^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T82a = 1/q +q^3 +q^5 +q^7 +q^9 +2*q^11 +2*q^13 +2*q^15 +2*q^17 +...

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^41]*H[x] - x^8*H[x^41]*G[x]; a:= CoefficientList[Series[B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 02 2018 *)

Crossrefs

Sequence in context: A356068 A255405 A239508 * A018050 A194316 A261796

Adjacent sequences: A112207 A112208 A112209 * A112211 A112212 A112213

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved