A058725 McKay-Thompson series of class 60A for the Monster group.

1, 2, 0, 1, 1, 3, 1, 6, 3, 5, 7, 9, 8, 14, 9, 17, 18, 24, 21, 33, 30, 40, 43, 54, 52, 77, 69, 93, 97, 117, 121, 160, 153, 191, 200, 246, 250, 319, 312, 381, 410, 480, 494, 607, 609, 733, 775, 903, 937, 1120, 1152, 1345, 1431, 1638, 1712, 2020, 2085, 2406

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of A + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^3)*eta(q^10) *eta(q^15)/(eta(q)*eta(q^5)*eta(q^6)*eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T60A = 1/q + 2*q + q^5 + q^7 + 3*q^9 + q^11 + 6*q^13 + 3*q^15 + 5*q^17 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^3]* eta[q^10]*eta[q^15]/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30]));  a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30))); Vec(A + q/A) \\ G. C. Greubel, Jun 28 2018

Crossrefs

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

Sequence in context: A029347 A303427 A176076 * A068446 A253830 A167625

Adjacent sequences: A058722 A058723 A058724 * A058726 A058727 A058728

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Status

approved