A058727 McKay-Thompson series of class 60C for Monster.

1, 0, 1, 1, 2, 2, 2, 3, 5, 5, 5, 7, 9, 10, 11, 14, 18, 20, 22, 27, 32, 36, 40, 48, 57, 63, 70, 82, 95, 106, 119, 137, 158, 175, 195, 222, 252, 280, 311, 352, 397, 439, 486, 546, 611, 676, 747, 834, 929, 1024, 1128, 1253, 1389, 1528, 1679, 1857, 2052, 2250, 2467, 2718

Offset

-1,5

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

a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of (eta(q^6)*eta(q^10))^3 /(eta(q^2)*eta(q^3)* eta(q^5)* eta(q^12)*eta(q^20)* eta(q^30)) in powers of q. - G. C. Greubel, Jan 23 2018

Example

T60C = 1/q + q + q^2 + 2*q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 5*q^7 + 5*q^8 + 5*q^9 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[(eta[q^6]* eta[q^10])^3 /(eta[q^2]*eta[q^3]* eta[q^5]*eta[q^12]*eta[q^20]* eta[q^30]), {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 23 2018 *)

Crossrefs

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

Cf. A145725 (same sequence except for n=0).

Sequence in context: A058618 A135213 A145725 * A304683 A035658 A077018

Adjacent sequences: A058724 A058725 A058726 * A058728 A058729 A058730

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved