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A112210 McKay-Thompson series of class 82a for the Monster group. 1
1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 9, 9, 11, 12, 14, 15, 18, 19, 22, 24, 27, 29, 34, 36, 41, 44, 50, 54, 61, 65, 73, 79, 88, 95, 106, 114, 126, 136, 150, 162, 179, 192, 211, 228, 249, 268, 294, 316, 345, 371, 404, 434, 473, 507, 551, 592, 641, 688 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,7

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of G(q^41)*H(q) - q^8*H(q^41)*G(q) in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(2*Pi*sqrt(2*n/41)) / (2^(3/4) * 41^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T82a = 1/q +q^3 +q^5 +q^7 +q^9 +2*q^11 +2*q^13 +2*q^15 +2*q^17 +...

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];

B := G[x^41]*H[x] - x^8*H[x^41]*G[x]; a:= CoefficientList[Series[B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 02 2018 *)

CROSSREFS

Sequence in context: A300270 A255405 A239508 * A018050 A194316 A261796

Adjacent sequences:  A112207 A112208 A112209 * A112211 A112212 A112213

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified October 18 15:41 EDT 2019. Contains 328162 sequences. (Running on oeis4.)