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A058538 McKay-Thompson series of class 18c for Monster. 1
1, 3, 9, 16, 33, 54, 98, 150, 243, 364, 564, 828, 1221, 1749, 2511, 3528, 4938, 6804, 9358, 12714, 17217, 23068, 30822, 40824, 53916, 70659, 92340, 119912, 155277, 199980, 256792, 328218, 418311, 530960, 672072, 847584, 1066157, 1336686, 1671741, 2084464, 2593059, 3216834, 3981926 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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 q^(1/2)*(eta(q^3)^2/(eta(q)*eta(q^9)))^3 in powers of q. - G. C. Greubel, Jun 20 2018

a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T18c = 1/q + 3*q + 9*q^3 + 16*q^5 + 33*q^7 + 54*q^9 + 98*q^11 + 150*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q^3]^2/(eta[q]*eta[q^9]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^50); Vec((eta(q^3)^2/(eta(q)*eta(q^9)))^3) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

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

Sequence in context: A212870 A257034 A232167 * A197531 A117108 A223188

Adjacent sequences:  A058535 A058536 A058537 * A058539 A058540 A058541

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 20 2018

STATUS

approved

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Last modified January 20 21:36 EST 2019. Contains 319336 sequences. (Running on oeis4.)