A112176 McKay-Thompson series of class 36f for the Monster group.

1, -1, 1, 0, 1, -2, 2, -2, 3, -4, 4, -4, 5, -7, 7, -8, 10, -12, 14, -14, 17, -20, 22, -24, 28, -33, 36, -40, 45, -52, 56, -62, 71, -80, 88, -96, 109, -122, 133, -144, 163, -182, 198, -216, 240, -268, 290, -316, 349, -386, 420, -456, 502, -552, 600, -650, 713, -780, 846, -916, 1001, -1093, 1182

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

Expansion of q^(1/2)*(eta(q)*eta(q^6)^4*eta(q^9)/(eta(q^2)*eta(q^3)* eta(q^18))^2) in powers of q. - G. C. Greubel, Jun 19 2018

a(n) ~ (-1)^n * exp(Pi*sqrt(2*n)/3) / (2^(5/4)*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T36f = 1/q - q + q^3 + q^7 - 2*q^9 + 2*q^11 - 2*q^13 + 3*q^15 - 4*q^17 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= SeriesCoefficient[q^(1/2)*(eta[q] *eta[q^6]^4*eta[q^9]/(eta[q^2]*eta[q^3]*eta[q^18])^2), {q, 0, n}];  Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); Vec((eta(q)*eta(q^6)^4*eta(q^9)/(eta(q^2)*eta(q^3)* eta(q^18))^2)) \\ G. C. Greubel, Jun 19 2018

Crossrefs

Sequence in context: A285763 A294621 A029077 * A112205 A369573 A117953

Adjacent sequences: A112173 A112174 A112175 * A112177 A112178 A112179

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved