A058768 McKay-Thompson series of class 94A for the Monster group.

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

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