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A058708 McKay-Thompson series of class 54A for the Monster group. 1
1, 0, 1, 1, 3, 2, 4, 3, 6, 5, 9, 8, 14, 12, 19, 18, 27, 26, 37, 36, 52, 50, 69, 68, 93, 93, 122, 124, 162, 164, 210, 216, 274, 281, 351, 364, 451, 468, 572, 598, 726, 760, 913, 960, 1148, 1208, 1431, 1512, 1782, 1884, 2206, 2339, 2727, 2892, 3353, 3564, 4114 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

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 -1 + A*B/x in powers of q, where A = G(x^54)*G(x) + x^11* H(x^54)*H(x), B = G(x^27)*H(x^2) - x^5*H(x^27)*G(x^2), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(2*Pi*sqrt(2*n/3)/3) / (6^(3/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T54A = 1/q + q + q^2 + 3*q^3 + 2*q^4 + 4*q^5 + 3*q^6 + 6*q^7 + 5*q^8 + 9*q^9 + ...

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^54]*G[x^1] + x^11*H[x^54]*H[x^1]; B:= G[x^27]*H[x^2] - x^5*H[x^27]*G[x^2]; a:= CoefficientList[Series[-x + 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: A133131 A261985 A026923 * A141731 A294145 A024856

Adjacent sequences:  A058705 A058706 A058707 * A058709 A058710 A058711

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 22 18:53 EST 2019. Contains 319365 sequences. (Running on oeis4.)