A058568 McKay-Thompson series of class 22B for Monster.

1, 0, 1, -2, 4, -4, 5, -6, 9, -12, 13, -18, 25, -28, 33, -44, 54, -64, 74, -92, 114, -132, 155, -186, 224, -260, 303, -360, 424, -488, 565, -662, 770, -888, 1018, -1180, 1366, -1560, 1780, -2048, 2345, -2668, 3034, -3460, 3946, -4468, 5052, -5734, 6502, -7328, 8255, -9320, 10512, -11808

Offset

-1,4

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

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/11)) / (2*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

Expansion of 2 + (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2 in powers of q. - G. C. Greubel, Jun 18 2018

Example

T22B = 1/q + q - 2*q^2 + 4*q^3 - 4*q^4 + 5*q^5 - 6*q^6 + 9*q^7 - 12*q^8 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[2 + (eta[q]*eta[q^11]/(eta[q^2]*eta[q^22]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Prog

(PARI) q='q+O('q^50); A = 2 +(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

Crossrefs

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

Cf. A132320 (same sequence except for n=0).

Sequence in context: A133143 A085898 A058679 * A339769 A147534 A118001

Adjacent sequences: A058565 A058566 A058567 * A058569 A058570 A058571

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved