A058666 McKay-Thompson series of class 40b for Monster.

1, -2, -1, -2, 0, -2, -1, -4, 1, -4, -2, -8, 2, -10, -1, -12, 3, -16, -3, -20, 3, -28, -3, -34, 4, -42, -5, -52, 5, -64, -7, -84, 8, -100, -8, -120, 9, -148, -10, -176, 13, -218, -15, -260, 14, -308, -17, -368, 20, -436, -23, -524, 24, -616, -26, -724, 31, -852, -34, -996, 38, -1178

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 - 2*q/A, where A = q^(1/2)*eta(q^2)*eta(q^10)/(eta(q^4)* eta(q^20)), in powers of q. - G. C. Greubel, Jun 19 2018

Example

T40b = 1/q - 2*q - q^3 - 2*q^5 - 2*q^9 - q^11 - 4*q^13 + q^15 - 4*q^17 - ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^10])/( eta[q^4]*eta[q^20]); a:= CoefficientList[Series[A - 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^10)/(eta(q^4)*eta(q^20)); Vec(A - 2*q/A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

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

Sequence in context: A118054 A322019 A077883 * A112181 A151676 A151684

Adjacent sequences: A058663 A058664 A058665 * A058667 A058668 A058669

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 19 2018

Status

approved