A058546 McKay-Thompson series of class 18h for Monster.

1, 0, 4, -2, 0, 8, 1, 0, 12, -4, 0, 32, 8, 0, 52, -6, 0, 80, 10, 0, 148, -16, 0, 224, 18, 0, 332, -26, 0, 536, 33, 0, 784, -40, 0, 1120, 58, 0, 1676, -74, 0, 2368, 82, 0, 3296, -112, 0, 4704, 147, 0, 6472, -166, 0, 8808, 212, 0, 12160, -268, 0, 16384, 316, 0, 21884, -392, 0, 29472, 476

Offset

-1,3

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^2/A, where A = q*(eta(q^3)*eta(q^9)/(eta(q^6) *eta(q^18)))^2, in powers of q. - G. C. Greubel, Jun 21 2018

Example

T18h = 1/q + 4*q - 2*q^2 + 8*q^4 + q^5 + 12*q^7 - 4*q^8 + 32*q^10 + 8*q^11 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^9]/(eta[q^6] *eta[q^18]))^2; a:= CoefficientList[Series[A + 4*q^2/A, {q, 0, 80}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

Prog

(PARI) q='q+O('q^60); A = (eta(q^3)*eta(q^9)/(eta(q^6)*eta(q^18)))^2; Vec(A + 4*q^2/A) \\ G. C. Greubel, Jun 21 2018

Crossrefs

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

Sequence in context: A245970 A197813 A200496 * A196774 A219245 A299769

Adjacent sequences: A058543 A058544 A058545 * A058547 A058548 A058549

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(24) onward added by G. C. Greubel, Jun 21 2018

Status

approved