A058636 McKay-Thompson series of class 33A for Monster.

1, 0, -1, 1, -1, 0, 2, -1, -1, 3, -2, -2, 5, -2, -3, 6, -4, -4, 9, -5, -7, 12, -7, -7, 18, -9, -10, 22, -13, -14, 31, -16, -18, 39, -22, -24, 53, -28, -31, 66, -37, -38, 87, -46, -51, 108, -59, -64, 138, -74, -80, 171, -94, -100, 216, -115, -126, 266, -144

Offset

-1,7

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of 1 + eta(q)*eta(q^11)/(eta(q^3)*eta(q^33)), in powers of q. - G. C. Greubel, Jun 19 2018

Example

T33A = 1/q - q + q^2 - q^3 + 2*q^5 - q^6 - q^7 + 3*q^8 - 2*q^9 - 2*q^10 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^11])/(eta[q^3] *eta[q^33]); a := CoefficientList[Series[1 + 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 = 1 + eta(q)*eta(q^11)/(eta(q^3)*eta(q^33))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

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

Cf. A226009 (same sequence except for n=0).

Sequence in context: A110248 A094340 A228668 * A226009 A132462 A161039

Adjacent sequences: A058633 A058634 A058635 * A058637 A058638 A058639

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved