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A058503 McKay-Thompson series of class 14B for Monster. 3
1, 0, 3, -4, 9, -12, 15, -24, 39, -52, 66, -96, 130, -168, 219, -292, 390, -492, 625, -804, 1023, -1280, 1599, -2016, 2508, -3096, 3807, -4688, 5760, -7020, 8532, -10368, 12585, -15156, 18213, -21912, 26287, -31404, 37410, -44584, 53004, -62784, 74245, -87768, 103578 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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

a(n) = -(-1)^n * exp(2*Pi*sqrt(n/7)) / (2*7^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of F - 1 + 4/F, where F = (eta(q^2)*eta(q^14))^3/(eta(q)*eta(q^7)*(eta(q^4)*eta(q^28))^2), in powers of q. - G. C. Greubel, Jun 13 2018

EXAMPLE

T14B = 1/q + 3*q - 4*q^2 + 9*q^3 - 12*q^4 + 15*q^5 - 24*q^6 + 39*q^7 - ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; b:= (eta[q^2]*eta[q^14])^3/(eta[q]*

eta[q^7]*(eta[q^4]*eta[q^28])^2); a:= CoefficientList[Series[q*(b  -1 + 4/b), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 13 2018 *)

PROG

(PARI) q='q+O('q^30); A = q^(-1)*(eta(q^2)*eta(q^14))^3/(eta(q)*eta(q^7)*(eta(q^4)*eta(q^28))^2); Vec(A -1 + 4/A) \\ G. C. Greubel, Jun 13 2018

CROSSREFS

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

Cf. A132319 (same sequence except for n=0).

Sequence in context: A010394 A010427 A127163 * A112169 A155564 A105137

Adjacent sequences:  A058500 A058501 A058502 * A058504 A058505 A058506

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 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)