A058600 McKay-Thompson series of class 27a for Monster.

1, 0, 3, -1, 0, 3, -1, 0, 6, 0, 0, 9, 0, 0, 15, 1, 0, 21, 0, 0, 33, 1, 0, 45, 0, 0, 66, 1, 0, 87, -1, 0, 123, -1, 0, 162, -1, 0, 222, 0, 0, 288, 1, 0, 384, -1, 0, 495, 1, 0, 648, 0, 0, 825, 2, 0, 1062, -2, 0, 1341, -2, 0, 1707, -1, 0, 2136, 1, 0, 2688, 2, 0, 3339, -1, 0, 4164, 2, 0, 5136, 1, 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 + 3*q^2/A, where A = q*(eta(q^3)/eta(q^27)), in powers of q. - G. C. Greubel, Jun 22 2018

Example

T27a = 1/q + 3*q - q^2 + 3*q^4 - q^5 + 6*q^7 + 9*q^10 + 15*q^13 + q^14 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q];  A:= q*(eta[q^3]/eta[q^27]);  a:= CoefficientList[Series[A + 3*q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 22 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^3)/eta(q^27); Vec(A + 3*q^2/A) \\ G. C. Greubel, Jun 22 2018

Crossrefs

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

Sequence in context: A068464 A244679 A035674 * A133704 A160019 A227054

Adjacent sequences: A058597 A058598 A058599 * A058601 A058602 A058603

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(24) onward added by G. C. Greubel, Jun 22 2018

Status

approved