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A058612 McKay-Thompson series of class 30A for Monster. 2
1, 0, 3, -1, 0, 0, 0, -3, 9, -9, 3, -3, 9, -12, 15, -18, 12, -6, 18, -39, 48, -46, 36, -24, 37, -75, 96, -90, 81, -78, 99, -165, 222, -199, 147, -150, 208, -306, 411, -424, 345, -327, 442, -606, 735, -756, 645, -606, 837, -1182, 1386, -1405, 1281, -1188, 1451 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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 3 + ((eta(q)*eta(q^6)*eta(q^10)*eta(q^15))/(eta(q^2) *eta(q^3)*eta(q^5)*eta(q^30)))^3 in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T30A = 1/q + 3*q - q^2 - 3*q^6 + 9*q^7 - 9*q^8 + 3*q^9 - 3*q^10 + 9*q^11 - ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q]*eta[q^6]*eta[q^10]* eta[q^15])/(eta[q^2]*eta[q^3]*eta[q^5]*eta[q^30]))^3; a:= CoefficientList[Series[3 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = 3 + ((eta(q)*eta(q^6)*eta(q^10) *eta(q^15))/( eta(q^2)*eta(q^3)*eta(q^5)*eta(q^30)))^3/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

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

Cf. A205826 (same sequence except for n=0).

Sequence in context: A286131 A285631 A316836 * A099725 A285118 A128208

Adjacent sequences:  A058609 A058610 A058611 * A058613 A058614 A058615

KEYWORD

sign

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 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)