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A045490 McKay-Thompson series of class 8A for Monster. 3
1, 4, 36, 128, 386, 1024, 2488, 5632, 12031, 24576, 48308, 91904, 170110, 307200, 542872, 941056, 1602819, 2686976, 4439688, 7238272, 11657090, 18561024, 29242240, 45617664, 70507772, 108036096, 164192188, 247620352, 370726652, 551215104, 814216536, 1195226112, 1744133125, 2530738176 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

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

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

FORMULA

From Vaclav Kotesovec, Sep 07 2017: (Start)

a(n) = A007265(n) unless n=0.

a(n) ~ exp(sqrt(2*n)*Pi) / (2^(5/4) * n^(3/4)). (End)

Expansion of -4 + (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^8 in powers of q. - G. C. Greubel, Jun 02 2018

MATHEMATICA

nmax = 50; CoefficientList[Series[-4*x + Product[((1 - x^(2*k))*(1 - x^(4*k))/((1 - x^k)*(1 - x^(8*k))))^8, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2017 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-4 + (eta[q^2]*eta[q^4]/(eta[q]*eta[q^8]))^8), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 02 2018 *)

PROG

(PARI) q='q+O('q^30); a= -4 + (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^8/q; Vec(a) \\ G. C. Greubel, Jun 02 2018

CROSSREFS

Cf. A007265.

Sequence in context: A076830 A144298 A072109 * A318150 A275133 A060783

Adjacent sequences:  A045487 A045488 A045489 * A045491 A045492 A045493

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 06:34 EST 2019. Contains 319207 sequences. (Running on oeis4.)