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A112217 McKay-Thompson series of class 93A for the Monster group. 2
1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 9, 10, 12, 12, 14, 15, 17, 18, 21, 22, 25, 27, 30, 32, 36, 38, 43, 46, 51, 54, 60, 64, 71, 76, 83, 89, 98, 104, 114, 122, 133, 142, 155, 165, 180, 192, 208, 222, 241, 256, 278, 296, 320, 341, 368, 391, 422 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Also McKay-Thompson series of class 93B for Monster. - Michel Marcus, Feb 19 2014

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..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).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of G(q^31)*H(q) - q^6*H(q^31)*G(q) in powers of q, where 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/93)) / (sqrt(2) * 93^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T93A = 1/q +q^5 +q^8 +q^11 +q^14 +q^17 +q^20 +2*q^23 +2*q^26 +...

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^31]*H[x] - x^6*H[x^31]*G[x]; a:= CoefficientList[Series[B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 29 2018 *)

CROSSREFS

Sequence in context: A280950 A279135 A053266 * A172033 A214131 A229977

Adjacent sequences:  A112214 A112215 A112216 * A112218 A112219 A112220

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)