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A058514 McKay-Thompson series of class 16A for Monster. 1
1, 4, 10, 24, 47, 84, 150, 248, 403, 648, 1002, 1536, 2316, 3420, 5004, 7224, 10309, 14592, 20456, 28440, 39240, 53736, 73102, 98808, 132779, 177444, 235868, 312024, 410785, 538368, 702630, 913208, 1182342, 1525200, 1960418, 2511360, 3206675, 4081576, 5179670, 6554112, 8270086 (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^2)*eta(q^4)/(eta(q)*eta(q^8)))^4 in powers of q. - G. C. Greubel, Jun 20 2018

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

EXAMPLE

T16A = 1/q + 4*q + 10*q^3 + 24*q^5 + 47*q^7 + 84*q^9 + 150*q^11 + 248*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^4]/(eta[q]*eta[q^8]))^4, {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

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

Sequence in context: A174934 A083168 A143696 * A182094 A291949 A001979

Adjacent sequences:  A058511 A058512 A058513 * A058515 A058516 A058517

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 October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)