A058484 McKay-Thompson series of class 12F for Monster.

1, 6, 21, 56, 126, 258, 498, 924, 1659, 2884, 4872, 8028, 12965, 20586, 32187, 49616, 75468, 113412, 168590, 248148, 361929, 523348, 750660, 1068576, 1510428, 2120934, 2959692, 4105808, 5663814, 7771452, 10609576, 14414676, 19494855, 26249984, 35197536

Offset: 0

Author

N. J. A. Sloane, Nov 27 2000

Keywords

• nonn

Examples

			T12F = 1/q + 6*q + 21*q^3 + 56*q^5 + 126*q^7 + 258*q^9 + 498*q^11 + ...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..148 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 = 50; CoefficientList[Series[Product[((1+x^(3*k-1))*(1+x^(3*k-2)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 10 2015 *)
eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^6; a := CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

PARI

q='q+O('q^66); Vec( eta(q^2)^6*eta(q^3)^6 / (eta(q)^6*eta(q^6)^6) )  \\ Joerg Arndt, Mar 13 2017

Formula

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 10 2015

From G. A. Edgar, Mar 13 2017: (Start)

Expansion of q^(1/2)*(eta(q^2)*eta(q^3) / (eta(q)*eta(q^6)))^6 in powers of q.

T12F(q) = T6B(q^2)^(1/2) with T6B the g.f. of A121665, the convolution square of A058484. (End)

Extensions

More terms from Vaclav Kotesovec, Sep 10 2015