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A058704 McKay-Thompson series of class 51A for the Monster group. 2
1, 0, 1, 2, 2, 2, 5, 4, 6, 8, 9, 10, 17, 16, 19, 26, 29, 34, 46, 48, 59, 72, 80, 92, 117, 126, 148, 178, 198, 226, 274, 298, 345, 404, 450, 510, 601, 660, 753, 866, 965, 1084, 1253, 1378, 1558, 1770, 1965, 2196, 2501, 2752, 3085, 3476, 3845, 4276, 4820, 5298 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..2500 from G. C. Greubel)

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A*B in powers of q, where A = G(q^17)*G(q^3) + q^4*H(q^17) *H(q^3), B = G(q^51)*H(q) - q^10*H(q^51)*G(q), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(4*Pi*sqrt(n/51)) / (sqrt(2) * 51^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T51A = 1/q + q + 2*q^2 + 2*q^3 + 2*q^4 + 5*q^5 + 4*q^6 + 6*q^7 + 8*q^8 + ...

MATHEMATICA

QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A:= G[x^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; a := CoefficientList[Series[A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)

CROSSREFS

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

Sequence in context: A134634 A103286 A285704 * A316660 A098101 A257670

Adjacent sequences:  A058701 A058702 A058703 * A058705 A058706 A058707

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 October 17 22:16 EDT 2019. Contains 328134 sequences. (Running on oeis4.)