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A058553 McKay-Thompson series of class 20D for Monster. 1
1, -2, 1, -2, 4, -6, 9, -8, 13, -20, 22, -28, 34, -46, 57, -68, 87, -104, 127, -152, 187, -232, 267, -318, 388, -462, 545, -632, 753, -896, 1043, -1216, 1416, -1664, 1928, -2228, 2597, -2996, 3454, -3976, 4585, -5286, 6031, -6900, 7918, -9060, 10325, -11720, 13372, -15228, 17259, -19564 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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^5)/(eta(q^2)*eta(q^10)))^2  in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ -(-1)^n * exp(sqrt(2*n/5)*Pi) / (2^(5/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T20D = 1/q - 2*q + q^3 - 2*q^5 + 4*q^7 - 6*q^9 + 9*q^11 - 8*q^13 + 13*q^15 - ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^5]/(eta[q^2]*eta[q^10]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^60); A = (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^2; Vec(A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A301413 A305056 A112179 * A038067 A136102 A279586

Adjacent sequences:  A058550 A058551 A058552 * A058554 A058555 A058556

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

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)