A112213 McKay-Thompson series of class 88A for the Monster group.

1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 3, 4, 5, 6, 6, 6, 8, 9, 10, 10, 12, 14, 15, 16, 19, 21, 22, 24, 27, 31, 34, 36, 40, 46, 48, 52, 58, 64, 69, 74, 82, 91, 98, 104, 115, 127, 136, 145, 159, 174, 186, 200, 218, 238, 254, 272, 296, 322, 343, 366, 398, 430, 460, 492, 531

Offset

0,9

Comments

Also McKay-Thompson series of class 88B for Monster. - Michel Marcus, Feb 19 2014

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of q^(1/2)*((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4)*eta(q^11)* eta(q^44))) in powers of q. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T88A = 1/q +q +q^5 +q^7 +q^9 +q^11 +q^13 +2*q^15 +2*q^17 +...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*((eta[q^2]*eta[q^22])^2/ (eta[q]*eta[q^4]*eta[q^11]*eta[q^44])); a:= CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 02 2018 *)

Prog

(PARI) q='q+O('q^70); A = ((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4) *eta(q^11)*eta(q^44))); Vec(A) \\ G. C. Greubel, Jul 02 2018

Crossrefs

Sequence in context: A055034 A362739 A112184 * A238957 A238970 A085755

Adjacent sequences: A112210 A112211 A112212 * A112214 A112215 A112216

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved