A058661 - OEIS

A058661

McKay-Thompson series of class 39C for Monster.

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

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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