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A058206 McKay-Thompson series of class 12C for the Monster group. 2
1, 7, 15, 71, 106, 273, 486, 961, 1563, 3040, 4692, 8199, 12773, 20919, 31569, 50552, 74368, 114504, 167366, 250033, 358845, 527650, 745688, 1073784, 1504452, 2129317, 2947224, 4122518, 5644462, 7792122, 10585876, 14446420, 19450323, 26307536, 35131220, 47077341, 62449405, 82987854, 109317927, 144252191 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..128 from G. A. Edgar)

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

M. Somos, Emails to N. J. A. Sloane, 1993

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of q^(1/2)*(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^6 + (eta(q)*eta(q^6)/(eta(q^2)*eta(q^3)))^6 in powers of q. - G. A. Edgar, Mar 13 2017

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 18 2017

G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Jul 06 2018

EXAMPLE

T12C = 1/q + 7*q + 15*q^3 + 71*q^5 + 106*q^7 + 273*q^9 + 486*q^11 + ...

MATHEMATICA

QP := QPochhammer; CoefficientList[Series[QP[x^2]^6*QP[x^3]^6 / (QP[x]^6*QP[x^6]^6) + x*QP[x]^6*QP[x^6]^6 / (QP[x^2]^6*QP[x^3]^6), {x, 0, 66}], x] (* Indranil Ghosh, Mar 14 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]* eta[q^3]/( eta[q]*eta[q^6]))^6; a := CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)

a[ n_] := With[{A = (QPochhammer[ x^3, x^6] / QPochhammer[ x, x^2])^6 },

SeriesCoefficient[ A + x / A, {x, 0, n}]]; (* Michael Somos, Jul 06 2018 )

PROG

(PARI) q='q+O('q^66); Vec( eta(q^2)^6*eta(q^3)^6 / (eta(q)^6*eta(q^6)^6) + q* eta(q)^6*eta(q^6)^6 / (eta(q^2)^6*eta(q^3)^6) )  \\ Joerg Arndt, Mar 13 2017

CROSSREFS

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

Sequence in context: A279882 A171064 A042313 * A219523 A177128 A177177

Adjacent sequences:  A058203 A058204 A058205 * A058207 A058208 A058209

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from G. A. Edgar, Mar 13 2017

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)