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A058680 McKay-Thompson series of class 44a for Monster. 1
1, -3, -2, -3, -3, -5, -5, -9, -8, -14, -14, -23, -22, -35, -34, -53, -52, -76, -78, -110, -111, -154, -162, -216, -226, -297, -316, -407, -433, -550, -590, -739, -793, -986, -1066, -1306, -1408, -1720, -1860, -2246, -2436, -2919, -3170, -3774, -4101, -4856, -5288, -6213, -6769 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1500

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 - 2*q/A, where A = q^(1/2)*(eta(q)*eta(q^11)/( eta(q^2)* eta(q^22))), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ -exp(2*Pi*sqrt(n/11)) / (2 * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T44a = 1/q - 3*q - 2*q^3 - 3*q^5 - 3*q^7 - 5*q^9 - 5*q^11 - 9*q^13 - 8*q^15 - ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^11]/( eta[q^2]*eta[q^22])); a:= CoefficientList[Series[A - 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)); Vec(A - 2*q/A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A234300 A181672 A125748 * A070544 A087713 A089319

Adjacent sequences:  A058677 A058678 A058679 * A058681 A058682 A058683

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 27 2018

STATUS

approved

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Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)