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A134785 McKay-Thompson series of class 8A for the Monster group with a(0) = 2. 1
1, 2, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

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

M. Koike, Mathieu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Associated with permutations in Mathieu group M24 of shape (8)^2(4)(2)(1)^2.

G.f. is Fourier series of a level 8 modular function. f(-1/ (8 t)) = f(t) where q = exp(2 Pi i t).

a(n) ~ exp(sqrt(2*n)*Pi) / (2^(5/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of -6 + (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^8 in powers of q. - G. C. Greubel, Jun 20 2018

EXAMPLE

1/q + 2 + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...

MATHEMATICA

QP = QPochhammer; s = -6*q + (QP[q^2]^8*QP[q^4]^8)/(QP[q]^8*QP[q^8]^8) + O[q]^30; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 16 2015, adapted from PARI *)

PROG

(PARI) {a(n) = local(A); if( n<-1, 0, A = x^2 * O(x^n); polcoeff( -6 + ( eta(x^2 + A) * eta(x^4 + A) / eta(x + A) / eta(x^8 + A) )^8 / x, n))}

CROSSREFS

A007265(n) = a(n) unless n=0. Convolution with A030207 is A029713.

Cf. A131123, A045490. [From R. J. Mathar, Dec 13 2008]

Sequence in context: A145450 A196558 A187509 * A143745 A199944 A227927

Adjacent sequences:  A134782 A134783 A134784 * A134786 A134787 A134788

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 22 2007

STATUS

approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)