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

0,2

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

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)

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A243740 A369794 A137361 * A145455 A346893 A337895

Adjacent sequences: A058481 A058482 A058483 * A058485 A058486 A058487

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Vaclav Kotesovec, Sep 10 2015

Status

approved