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A058761 McKay-Thompson series of class 84a for Monster. 1
1, -2, -1, -1, -1, -2, -1, -2, -2, -2, -2, -4, -3, -5, -4, -5, -5, -9, -6, -11, -9, -11, -11, -16, -13, -21, -19, -22, -22, -31, -25, -38, -35, -42, -41, -53, -48, -66, -62, -73, -75, -92, -84, -111, -107, -126, -127, -154, -145, -182, -180, -205, -211, -251, -242, -293, -291, -334 (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 - q/A, where A = q^(1/2)*(eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ -exp(2*Pi*sqrt(n/21)) / (2 * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 10 2018

EXAMPLE

T84a = 1/q - 2*q - q^3 - q^5 - q^7 - 2*q^9 - q^11 - 2*q^13 - 2*q^15 - 2*q^17 - ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^6] *eta[q^14]*eta[q^21]/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42])); a:= CoefficientList[Series[ Simplify[A - q/A, q>0] , {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))); Vec(A - q/A) \\ G. C. Greubel, Jun 30 2018

CROSSREFS

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

Sequence in context: A082370 A005136 A138474 * A050119 A290253 A097637

Adjacent sequences:  A058758 A058759 A058760 * A058762 A058763 A058764

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 30 2018

STATUS

approved

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Last modified January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)