A045486 McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).

1, 2, 15, -32, 87, -192, 343, -672, 1290, -2176, 3705, -6336, 10214, -16320, 25905, -39936, 61227, -92928, 138160, -204576, 300756, -435328, 626727, -897408, 1271205, -1790592, 2508783, -3487424, 4824825, -6641664, 9083400, -12371904, 16778784, -22630912, 30407112, -40703040, 54238342, -72018624, 95300769

Offset

-1,2

Comments

For n>0 same as A121666. - Vaclav Kotesovec, Apr 09 2016

Links

G. C. Greubel, Table of n, a(n) for n = -1..1001

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ (-1)^(n+1) * exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Apr 09 2016

Expansion of 8 + (eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^6. - G. C. Greubel, Jun 02 2018

Mathematica

nmax = 50; CoefficientList[Series[8*x + Product[((1-x^k)*(1-x^(3*k))/((1-x^(2*k))*(1-x^(6*k))))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2016 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q*(8 + (eta[q]*eta[q^3]/(eta[q^2]*eta[q^6]))^6), {q, 0, 60}], q]; Table[ a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 02 2018 *)

Prog

(PARI) N=66; q='q+O('q^N); Vec( ((eta(q^1)*eta(q^3))/(eta(q^2)*eta(q^6)))^6/q + 8 ) \\ Joerg Arndt, Apr 09 2016

Crossrefs

Cf. A007256.

Sequence in context: A154790 A042461 A196263 * A243469 A366330 A300431

Adjacent sequences: A045483 A045484 A045485 * A045487 A045488 A045489

Keyword

sign

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, Apr 09 2016

Status

approved