A045485 McKay-Thompson series of class 6B for Monster with a(0) = 7.

1, 7, 78, 364, 1365, 4380, 12520, 32772, 80094, 185276, 409578, 871272, 1792754, 3582708, 6977100, 13277472, 24747867, 45267324, 81389908, 144048396, 251265288, 432425864, 734953116, 1234647216, 2051576037

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.

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

Expansion of -5 + (eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12 in powers of q. - G. C. Greubel, Jun 12 2018

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-5 + (eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^12), {q, 0, 60}], q];
Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 12 2018 *)

Prog

(PARI) q='q+O('q^30); A=-5+(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(A) \\ G. C. Greubel, Jun 12 2018

Crossrefs

Cf. A007255.

Sequence in context: A356437 A107047 A210413 * A068621 A210406 A133272

Adjacent sequences: A045482 A045483 A045484 * A045486 A045487 A045488

Keyword

nonn

Author

N. J. A. Sloane

Status

approved