A058606 McKay-Thompson series of class 28A for Monster.

1, 3, 1, 7, 7, 18, 18, 35, 38, 65, 71, 119, 140, 207, 240, 356, 409, 581, 679, 946, 1100, 1493, 1738, 2307, 2704, 3528, 4134, 5314, 6221, 7907, 9233, 11613, 13566, 16907, 19700, 24336, 28350, 34716, 40379, 49140, 57090, 68991, 80021, 96188, 111357, 133156, 153923, 183194, 211422

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, Commun. 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 18 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 + 3*q + q^3 + 7*q^5 + 7*q^7 + 18*q^9 + 18*q^11 + 35*q^13 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; e28D:= q^(1/2)*((eta[q^2]*eta[q^7])/(eta[q]*eta[q^14]))^2; a[n_]:= SeriesCoefficient[e28D + q/e28D, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 18 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 18 2018

Crossrefs

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

Sequence in context: A359576 A319298 A101748 * A135284 A016647 A091039

Adjacent sequences: A058603 A058604 A058605 * A058607 A058608 A058609

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Feb 18 2018

Status

approved