A058510 McKay-Thompson series of class 15C for Monster.

1, 0, 9, 19, 42, 78, 146, 249, 429, 695, 1125, 1749, 2713, 4086, 6123, 8986, 13122, 18852, 26934, 38001, 53328, 74068, 102336, 140208, 191153, 258741, 348606, 466806, 622383, 825342, 1090087, 1432923, 1876542, 2447029, 3179859, 4116282, 5311204, 6829008

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 -3 + (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)))^3 in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(4*Pi*sqrt(n/15)) / (sqrt(2) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

Example

T15C = 1/q + 9*q + 19*q^2 + 42*q^3 + 78*q^4 + 146*q^5 + 249*q^6 + 429*q^7 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-3 + (eta[q^3]*eta[q^5]/(eta[q]*eta[q^15]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Prog

(PARI) q='q+O('q^50); A = -3 + (eta(q^3)*eta(q^5)/(eta(q)*eta(q^15)) )^3/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

Crossrefs

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

Cf. A153084 (same sequence except for n=0).

Sequence in context: A159697 A014005 A286624 * A043122 A043902 A048696

Adjacent sequences: A058507 A058508 A058509 * A058511 A058512 A058513

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 19 2014

Status

approved