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A058768 McKay-Thompson series of class 94A for the Monster group. 1
1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 5, 8, 6, 9, 8, 12, 10, 14, 12, 17, 15, 20, 18, 25, 22, 29, 27, 35, 32, 41, 38, 49, 46, 57, 54, 68, 64, 79, 76, 93, 89, 108, 104, 126, 122, 146, 142, 170, 165, 195, 192, 226, 222, 260, 256, 299, 296, 342 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,9

COMMENTS

Also McKay-Thompson series of class 94B for Monster. - Michel Marcus, Feb 24 2014

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..3200 (computed by David A. Madore)

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

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum, Aug 01 2007.

David A. Madore, Computation of Moonshine Coefficients

Index entries for McKay-Thompson series for Monster simple group

FORMULA

a(n) ~ exp(4*Pi*sqrt(n/94)) / (sqrt(2) * 94^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 10 2018

EXAMPLE

T94A = 1/q + q + q^3 + q^4 + q^5 + q^6 + 2*q^7 + q^8 + 2*q^9 + 2*q^10 + 3*q^11 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; Theta[a_, b_, c_] := Sum[q^((a*n^2 + b*n*m + c*m^2)/2), {n, -50, 50}, {m, -50, 50}]; T47A:= (Theta[2, 2, 24] - Theta[4, 2, 12])/(2*eta[q]*eta[q^47]); a:= CoefficientList[Series[ q*(T47A + (T47A /. {q -> q^2}) + T47A*(T47A /. {q -> q^2}))/(1 + T47A + (T47A /. {q -> q^2})), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 75}] (* G. C. Greubel, Jul 25 2018 *)

CROSSREFS

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

Sequence in context: A025799 A282537 A053267 * A127682 A127685 A127687

Adjacent sequences:  A058765 A058766 A058767 * A058769 A058770 A058771

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)