A058508 McKay-Thompson series of class 15A for Monster.

1, 0, 8, 22, 42, 70, 155, 246, 421, 722, 1101, 1730, 2761, 4062, 6106, 9040, 13065, 18806, 27081, 37950, 53183, 74290, 102213, 140048, 191612, 258426, 348300, 467484, 622023, 825016, 1090957, 1432290, 1875930, 2448610, 3179136, 4114996

Offset

-1,3

Links

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

Example

T15A = 1/q + 8*q + 22*q^2 + 42*q^3 + 70*q^4 + 155*q^5 + 246*q^6 + 421*q^7 + ...

Mathematica

QP = QPochhammer; A = QP[q]*(QP[q^5]/(QP[q^3]*QP[q^15])); s = -4q + (A + 3*(q/A))^2 + O[q]^40; CoefficientList[s, q] (* Jean-François Alcover, Nov 16 2015, adapted from A153765 *)

Prog

(PARI) q='q+O('q^30); F= (eta(q)*eta(q^5)/(eta(q^3)*eta(q^15)))^2; Vec(2*q + F + 9*q^2/F) \\ G. C. Greubel, Jun 03 2018

Crossrefs

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

Cf. A134783 (same sequence except for n=0).

Sequence in context: A063301 A030999 A113744 * A134783 A211529 A069099

Adjacent sequences: A058505 A058506 A058507 * A058509 A058510 A058511

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 19 2014

Status

approved