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A112213 McKay-Thompson series of class 88A for the Monster group. 1
1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 3, 4, 5, 6, 6, 6, 8, 9, 10, 10, 12, 14, 15, 16, 19, 21, 22, 24, 27, 31, 34, 36, 40, 46, 48, 52, 58, 64, 69, 74, 82, 91, 98, 104, 115, 127, 136, 145, 159, 174, 186, 200, 218, 238, 254, 272, 296, 322, 343, 366, 398, 430, 460, 492, 531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Also McKay-Thompson series of class 88B for Monster. - Michel Marcus, Feb 19 2014

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 q^(1/2)*((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4)*eta(q^11)* eta(q^44))) in powers of q. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T88A = 1/q +q +q^5 +q^7 +q^9 +q^11 +q^13 +2*q^15 +2*q^17 +...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*((eta[q^2]*eta[q^22])^2/ (eta[q]*eta[q^4]*eta[q^11]*eta[q^44])); a:= CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 02 2018 *)

PROG

(PARI) q='q+O('q^70); A = ((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4) *eta(q^11)*eta(q^44))); Vec(A) \\ G. C. Greubel, Jul 02 2018

CROSSREFS

Sequence in context: A060473 A055034 A112184 * A238957 A238970 A085755

Adjacent sequences:  A112210 A112211 A112212 * A112214 A112215 A112216

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified October 14 02:29 EDT 2019. Contains 327995 sequences. (Running on oeis4.)