A058556 McKay-Thompson series of class 20a for Monster.

1, -6, -7, -14, -20, -42, -55, -112, -139, -252, -314, -524, -678, -1042, -1335, -1980, -2553, -3688, -4681, -6592, -8341, -11520, -14557, -19626, -24692, -32834, -41135, -54016, -67279, -87328, -108285, -139176, -171984, -218808, -269296, -339844, -416715, -522236, -637642, -793736

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 -4*q/A, where A = q(1/2)*(eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ -exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T20a = 1/q - 6*q - 7*q^3 - 14*q^5 - 20*q^7 - 42*q^9 - 55*q^11 - 112*q^13 - ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q]*eta[q^5]/(eta[q^2]*eta[q^10]))^2; a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2; Vec(A - 4*q/A) \\ G. C. Greubel, Jun 21 2018

Crossrefs

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

Sequence in context: A315839 A315840 A315841 * A332045 A022311 A219382

Adjacent sequences: A058553 A058554 A058555 * A058557 A058558 A058559

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

Status

approved