A058677 McKay-Thompson series of class 42c for Monster.

1, 0, 2, -1, 0, 2, 0, 0, 2, -1, 0, 4, 1, 0, 4, -1, 0, 6, 1, 0, 8, -2, 0, 12, 3, 0, 14, -2, 0, 18, 3, 0, 24, -3, 0, 28, 4, 0, 36, -4, 0, 44, 4, 0, 56, -6, 0, 68, 7, 0, 82, -7, 0, 100, 7, 0, 120, -9, 0, 144, 10, 0, 172, -12, 0, 210, 13, 0, 248, -14, 0, 292, 17, 0, 348, -18, 0, 408, 19, 0

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 + 2*q^2/A, where A = q*(eta(q^3)*eta(q^21)/(eta(q^6) *eta(q^42))), in powers of q. - G. C. Greubel, Jun 26 2018

Example

T42c = 1/q + 2*q - q^2 + 2*q^4 + 2*q^7 - q^8 + 4*q^10 + q^11 + 4*q^13 - q^14 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^21]/(eta[q^6] *eta[q^42]));  a:= CoefficientList[Series[A + 2*q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) q='q+O('q^70); A = (eta(q^3)*eta(q^21)/(eta(q^6)*eta(q^42))); Vec(A + 2*q^2/A) \\ G. C. Greubel, Jun 26 2018

Crossrefs

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

Sequence in context: A112214 A246962 A112608 * A262780 A033762 A129449

Adjacent sequences: A058674 A058675 A058676 * A058678 A058679 A058680

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(24) onward added by G. C. Greubel, Jun 26 2018

Status

approved