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A058661 McKay-Thompson series of class 39C for Monster. 2
1, 0, 2, 2, 4, 5, 7, 9, 13, 16, 22, 27, 36, 43, 56, 68, 87, 104, 130, 156, 193, 230, 281, 333, 404, 477, 572, 673, 802, 940, 1113, 1299, 1531, 1780, 2085, 2418, 2820, 3259, 3784, 4362, 5047, 5799, 6685, 7662, 8806, 10066, 11532, 13152, 15026, 17098, 19482 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

Also McKay-Thompson series of class 39D for Monster. - Michel Marcus, Feb 19 2014

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -1 + (eta(q^3)*eta(q^13))/(eta(q)*eta(q^39)) in powers of q. - G. C. Greubel, Jun 19 2018

a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T39C = 1/q + 2*q + 2*q^2 + 4*q^3 + 5*q^4 + 7*q^5 + 9*q^6 + 13*q^7 + 16*q^8 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*((eta[q^3]*eta[q^13])/(eta[q]*eta[q^39]) - 1), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018*)

PROG

(PARI) q='q+O('q^50); Vec((eta(q^3)*eta(q^13))/(q*eta(q)*eta(q^39)) - 1) \\ G. C. Greubel, Jun 19 2018

CROSSREFS

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

Cf. A094362 (same sequence except for n=0).

Sequence in context: A007209 A240215 A166239 * A094362 A000726 A128663

Adjacent sequences:  A058658 A058659 A058660 * A058662 A058663 A058664

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 18 2014

STATUS

approved

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Last modified January 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)