A058205 McKay-Thompson series of class 11A for the Monster Group.

1, 0, 17, 46, 116, 252, 533, 1034, 1961, 3540, 6253, 10654, 17897, 29284, 47265, 74868, 117158, 180608, 275562, 415300, 620210, 916860, 1344251, 1953974, 2819664, 4038300, 5746031, 8122072, 11413112, 15943576, 22153909, 30620666

Offset

-1,3

Links

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

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

Expansion of -6 + (1 + 3*F)^2* (1/F + 1 + 3*F) where F = eta(q^3)* eta(q^33)/ (eta(q)* eta(q^11)) in powers of q.

G.f. is Fourier series of a level 11 modular function. f(-1 / (11t)) = f(t) where q = exp(2 Pi i t).

a(n) ~ exp(4*Pi*sqrt(n/11)) / (sqrt(2)*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Example

T11A = 1/q + 17*q + 46*q^2 + 116*q^3 + 252*q^4 + 533*q^5 + 1034*q^6 + ...

Mathematica

QP = QPochhammer; F = q*QP[q^3]*(QP[q^33]/(QP[q]*QP[q^11])); s = q*(-6 + (1 + 3*F)^2*(1/F + 1 + 3*F)) + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 15 2015 *)

Prog

(PARI) q='q+O('q^30); {F = q*(eta(q^3)*eta(q^33)/(eta(q)*eta(q^11)))};  Vec(-6 + (1+3*F)^2*(3*F + 1 +1/F)) \\ G. C. Greubel, May 28 2018

Crossrefs

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

Apart from initial terms, same as A003295.

Sequence in context: A120099 A307293 A045570 * A329951 A034783 A275770

Adjacent sequences: A058202 A058203 A058204 * A058206 A058207 A058208

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Status

approved