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A134784 McKay-Thompson series of class 11A for the Monster group with a(0) = 2. 2
1, 2, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666 (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 (11)^2(1)^2.

G.f. is a period 1 Fourier series which satisfies f(-1 / (11 t)) = f(t) where q = exp(2 Pi i t).

a(n) ~ exp(4*Pi*sqrt(n/11)) / (sqrt(2)*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of -4 + (1 + 3*F)^2* (1/F + 1 + 3*F) where F = eta(q^3)* eta(q^33)/ (eta(q)* eta(q^11)) in powers of q. - G. C. Greubel, Jun 17 2018

Expansion of 3 + (1 + A)*(16 + A^2)/A^2, where A = (eta(q)*eta(q^11)/ (eta(q^2)*eta(q^22)))^2, in powers of q. - G. C. Greubel, Jun 17 2018

EXAMPLE

G.f. = 1/q + 2 + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...

MATHEMATICA

QP = QPochhammer; F = q*QP[q^3]*(QP[q^33]/(QP[q]*QP[q^11])); s = q*(-4 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 16 2015, adapted from A058205 *)

PROG

(PARI) {a(n) = my(A); if( n<-1, 0, A = x^2 * O(x^n); A = (eta(x + A) * eta(x^11 + A) / ( eta(x^2 + A) * eta(x^22 + A) ))^2 / x; polcoeff( 3 + (1 + A) * (1 + 16 / A^2), n))};

CROSSREFS

A058205(n) = a(n) unless n=0. Convolution with A006571 is A028996.

Cf. A128525, A003295. [From R. J. Mathar, Dec 13 2008]

Sequence in context: A100271 A046973 A226488 * A023256 A073775 A141860

Adjacent sequences:  A134781 A134782 A134783 * A134785 A134786 A134787

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 22 2007

STATUS

approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)