A112209 McKay-Thompson series of class 80a for the Monster group.

1, 1, 0, 1, 1, 2, 2, 1, 3, 3, 3, 3, 4, 5, 5, 7, 8, 8, 9, 10, 13, 15, 14, 17, 20, 23, 24, 26, 31, 34, 38, 41, 46, 52, 55, 62, 70, 75, 82, 90, 103, 112, 118, 131, 145, 161, 172, 185, 208, 225, 244, 265, 288, 316, 339, 370, 404, 435, 469, 507, 557, 601, 640, 696, 755, 818

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

a(n) ~ exp(Pi*sqrt(n/5)) / (2^(3/2) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Expansion of q^(1/4)*(eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4)*eta(q^5) *eta(q^20)) in powers of q. - G. C. Greubel, Jun 20 2018

Example

T80a = 1/q +q^3 +q^11 +q^15 +2*q^19 +2*q^23 +q^27 +3*q^31 +...

Mathematica

nmax = 70; CoefficientList[Series[Product[(1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/4)*(eta[q^2]*eta[q^10])^2/( eta[q]*eta[q^4]*eta[q^5]*eta[q^20]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jun 20 2018 *)

Prog

(PARI) q='q+O('q^70); Vec((eta(q^2)*eta(q^10))^2/( eta(q)*eta(q^4) *eta(q^5)*eta(q^20))) \\ G. C. Greubel, Jun 20 2018

Crossrefs

Cf. A112182.

Sequence in context: A091224 A308684 A112182 * A240127 A109524 A191521

Adjacent sequences: A112206 A112207 A112208 * A112210 A112211 A112212

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved