A058485 McKay-Thompson series of class 12G for Monster.

1, -2, -3, 8, -2, -6, 18, -20, -21, 52, -24, -36, 101, -78, -93, 224, -116, -156, 398, -284, -327, 772, -412, -528, 1308, -866, -996, 2336, -1274, -1572, 3784, -2396, -2745, 6368, -3520, -4224, 9997, -6132, -6999, 16112, -8934, -10554, 24630, -14784, -16776, 38348, -21316, -24828, 57341, -33796

Offset

0,2

Comments

The convolution square of this sequence is A121667: T12G(q)^2 = T6D(q^2). - G. A. Edgar, Apr 15 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..502 from G. A. Edgar)

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 q^(1/2)*(eta(q)*eta(q^2)/(eta(q^3)*eta(q^6)))^2 in powers of q. - G. C. Greubel, Jun 18 2018

Example

T12G = 1/q - 2*q - 3*q^3 + 8*q^5 - 2*q^7 - 6*q^9 + 18*q^11 - 20*q^13 - ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2) (eta[q]*eta[q^2]/(eta[q^3]*eta[q^6]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 18 2018 *)

Prog

(PARI) q='q+O('q^50); Vec((eta(q)*eta(q^2)/(eta(q^3)*eta(q^6)))^2) \\ G. C. Greubel, Jun 18 2018

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, A121667, etc.

Sequence in context: A354861 A348261 A252651 * A204907 A183168 A011326

Adjacent sequences: A058482 A058483 A058484 * A058486 A058487 A058488

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Status

approved