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A058505 McKay-Thompson series of class 14a for Monster. 1
1, -9, -15, -33, -69, -138, -254, -453, -762, -1271, -2025, -3225, -4980, -7653, -11472, -17124, -25095, -36507, -52481, -74934, -105876, -148643, -206982, -286437, -393488, -537828, -730362, -987110, -1326579, -1775037, -2363135, -3133227, -4135902, -5438789, -7123452, -9296976 (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 A - 7*q/A, where A = q^(1/2)*(eta(q)/eta(q^7))^2, in powers of q. - G. C. Greubel, Jun 20 2018

a(n) ~ -exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T14a = 1/q - 9*q - 15*q^3 - 33*q^5 - 69*q^7 - 138*q^9 - 254*q^11 - ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]/eta[q^7])^2; a:= CoefficientList[Series[A - 7*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q)/eta(q^7))^2; Vec(A - 7*q/A) \\ G. C. Greubel, Jun 20 2018

CROSSREFS

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

Sequence in context: A228096 A111148 A125216 * A133763 A146475 A100556

Adjacent sequences:  A058502 A058503 A058504 * A058506 A058507 A058508

KEYWORD

sign

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 January 18 21:54 EST 2019. Contains 319282 sequences. (Running on oeis4.)