A058538 McKay-Thompson series of class 18c for Monster.

1, 3, 9, 16, 33, 54, 98, 150, 243, 364, 564, 828, 1221, 1749, 2511, 3528, 4938, 6804, 9358, 12714, 17217, 23068, 30822, 40824, 53916, 70659, 92340, 119912, 155277, 199980, 256792, 328218, 418311, 530960, 672072, 847584, 1066157, 1336686, 1671741, 2084464, 2593059, 3216834, 3981926

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^3)^2/(eta(q)*eta(q^9)))^3 in powers of q. - G. C. Greubel, Jun 20 2018

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

Example

T18c = 1/q + 3*q + 9*q^3 + 16*q^5 + 33*q^7 + 54*q^9 + 98*q^11 + 150*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q^3]^2/(eta[q]*eta[q^9]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)

Prog

(PARI) q='q+O('q^50); Vec((eta(q^3)^2/(eta(q)*eta(q^9)))^3) \\ G. C. Greubel, Jun 20 2018

Crossrefs

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

Sequence in context: A306447 A257034 A232167 * A197531 A117108 A223188

Adjacent sequences: A058535 A058536 A058537 * A058539 A058540 A058541

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