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A058679 McKay-Thompson series of class 44A for Monster. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

COMMENTS

Also McKay-Thompson series of class 44B for Monster. - Michel Marcus, Feb 24 2014

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).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -2 + ((eta(q^2)*eta(q^22))^2/( eta(q)*eta(q^4)*eta(q^11)* eta(q^44)))^2 in powers of q. - G. C. Greubel, Jun 26 2018

a(n) ~ exp(2*Pi*sqrt(n/11)) / (2 * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T44A = 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:= ((eta[q^2]*eta[q^22])^2/( eta[q]* eta[q^4]*eta[q^11] eta[q^44]))^2;  a:= CoefficientList[Series[-2 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

PROG

(PARI) q='q+O('q^50); F = -2 + ((eta(q^2)*eta(q^22))^2/( eta(q)*eta(q^4) *eta(q^11)*eta(q^44)))^2/q; Vec(F) \\ G. C. Greubel, Jun 26 2018

CROSSREFS

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

Sequence in context: A057861 A133143 A085898 * A058568 A147534 A118001

Adjacent sequences:  A058676 A058677 A058678 * A058680 A058681 A058682

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified October 17 15:01 EDT 2019. Contains 328116 sequences. (Running on oeis4.)