A058584 McKay-Thompson series of class 24a for Monster.

1, -5, -5, -9, -14, -19, -34, -55, -69, -104, -164, -209, -283, -413, -539, -712, -968, -1248, -1642, -2167, -2731, -3526, -4592, -5736, -7244, -9255, -11520, -14378, -18018, -22238, -27556, -34132, -41701, -51184, -62900, -76323, -92771, -113002, -136421, -164673, -198842, -238627

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..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 A - 4*q/A, where A = q^(1/2)*(eta(q)*eta(q^3)/(eta(q^4)* eta(q^12))), in powers of q. - G. C. Greubel, Jun 21 2018

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

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 4 * exp(-Pi / 2) * Gamma(3/4)^2 / Gamma(11/12) / Gamma(7/12) = A388448. - Simon Plouffe, Sep 15 2025

Example

T24a = 1/q - 5*q - 5*q^3 - 9*q^5 - 14*q^7 - 19*q^9 - 34*q^11 - 55*q^13 - ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^3]/( eta[q^4]*eta[q^12])); a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^3)/(eta(q^4)* eta(q^12))); Vec(A - 4*q/A) \\ G. C. Greubel, Jun 21 2018

Crossrefs

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

Cf. A058491.

Sequence in context: A011986 A047880 A058491 * A324792 A147197 A323301

Adjacent sequences: A058581 A058582 A058583 * A058585 A058586 A058587

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

Status

approved