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A058205 McKay-Thompson series of class 11A for the Monster Group. 4
1, 0, 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

-1,3

LINKS

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

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -6 + (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.f. is Fourier series of a level 11 modular function. f(-1 / (11t)) = 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

EXAMPLE

T11A = 1/q + 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*(-6 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 15 2015 *)

PROG

(PARI) q='q+O('q^30); {F = q*(eta(q^3)*eta(q^33)/(eta(q)*eta(q^11)))};  Vec(-6 + (1+3*F)^2*(3*F + 1 +1/F)) \\ G. C. Greubel, May 28 2018

CROSSREFS

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

Apart from initial terms, same as A003295.

Sequence in context: A032698 A120099 A045570 * A034783 A275770 A126912

Adjacent sequences:  A058202 A058203 A058204 * A058206 A058207 A058208

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)