A058610 McKay-Thompson series of class 28a for Monster.

1, 1, 5, 5, 11, 10, 26, 25, 46, 55, 91, 101, 156, 181, 272, 316, 457, 531, 747, 862, 1188, 1387, 1858, 2177, 2864, 3348, 4334, 5078, 6485, 7589, 9605, 11215, 14026, 16365, 20308, 23656, 29094, 33876, 41359, 48068, 58266, 67645, 81537, 94476, 113269, 131052, 156311, 180518

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 A - q/A, where A = q^(1/2)*(eta(q^2)*eta(q^7)/(eta(q)* eta(q^14)))^2, in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(2*Pi*sqrt(n/7)) / (2 * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T28a = 1/q + q + 5*q^3 + 5*q^5 + 11*q^7 + 10*q^9 + 26*q^11 + 25*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^7]/(eta[q]*eta[q^14]))^2; a:= CoefficientList[Series[(A - q/A), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jun 22 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 22 2018

Crossrefs

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

Sequence in context: A151728 A130889 A184827 * A143427 A287996 A239355

Adjacent sequences: A058607 A058608 A058609 * A058611 A058612 A058613

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 22 2018

Status

approved