A058492 McKay-Thompson series of class 12d for Monster.

1, -3, 3, -7, 18, -21, 30, -57, 75, -104, 156, -207, 293, -411, 525, -712, 984, -1248, 1622, -2169, 2757, -3530, 4560, -5736, 7284, -9249, 11472, -14374, 18078, -22242, 27484, -34140, 41787, -51184, 62796, -76317, 92893, -112998, 136275, -164671, 199014

Offset: 0

Author

N. J. A. Sloane, Nov 27 2000

Keywords

• sign

Comments

The convolution square of this sequence is A121666: T12d(q)^2 = T6C(q^2). - G. A. Edgar, Apr 15 2017

Examples

			T12d = 1/q - 3*q + 3*q^3 - 7*q^5 + 18*q^7 - 21*q^9 + 30*q^11 - 57*q^13 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500 (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

Crossrefs

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

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[((1 - x^(2*k-1)) * (1 - x^(6*k-3)))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 07 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^3]/(eta[q^2]*eta[q^6]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 03 2018 *)

PARI

{ my(q='q+O('q^66)); Vec( (eta(q)^3*eta(q^3)^3 / (eta(q^2)^3*eta(q^6)^3)) ) } \\ Joerg Arndt, Apr 16 2017

Formula

a(n) ~ (-1)^n * exp(Pi*sqrt(2*n/3)) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Nov 07 2015

Expansion of q^(1/2) * (eta(q)^3*eta(q^3)^3 / (eta(q^2)^3*eta(q^6)^3)) in powers of q. - G. A. Edgar, Apr 15 2017

Extensions

More terms from Vaclav Kotesovec, Nov 07 2015