A058514 McKay-Thompson series of class 16A for Monster.

1, 4, 10, 24, 47, 84, 150, 248, 403, 648, 1002, 1536, 2316, 3420, 5004, 7224, 10309, 14592, 20456, 28440, 39240, 53736, 73102, 98808, 132779, 177444, 235868, 312024, 410785, 538368, 702630, 913208, 1182342, 1525200, 1960418, 2511360, 3206675, 4081576, 5179670, 6554112, 8270086

Offset

-1,2

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of q^(1/2)*(eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4 in powers of q. - G. C. Greubel, Jun 20 2018

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

Example

T16A = 1/q + 4*q + 10*q^3 + 24*q^5 + 47*q^7 + 84*q^9 + 150*q^11 + 248*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^4]/(eta[q]*eta[q^8]))^4, {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 20 2018 *)

Prog

(PARI) q='q+O('q^50); Vec((eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4) \\ G. C. Greubel, Jun 20 2018

Crossrefs

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

Sequence in context: A174934 A083168 A143696 * A182094 A291949 A001979

Adjacent sequences: A058511 A058512 A058513 * A058515 A058516 A058517

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 20 2018

Status

approved