A058705 McKay-Thompson series of class 52A for Monster.

1, 0, 2, 2, 3, 2, 5, 4, 7, 6, 12, 10, 17, 14, 23, 24, 34, 32, 47, 46, 64, 64, 87, 88, 117, 118, 156, 160, 207, 212, 271, 280, 352, 366, 455, 476, 587, 612, 748, 788, 950, 1004, 1205, 1274, 1515, 1608, 1900, 2020, 2373, 2524, 2951, 3148, 3659, 3902, 4521, 4830, 5563, 5948, 6827, 7306, 8353

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, 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^13)/(eta(q)* eta(q^26))), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(2*Pi*sqrt(n/13)) / (2 * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T52A = 1/q + 2*q^3 + 2*q^5 + 3*q^7 + 2*q^9 + 5*q^11 + 4*q^13 + 7*q^15 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/(eta[q]*eta[q^26])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 27 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^2)*eta(q^13)/(eta(q)*eta(q^26)); Vec(A - q/A) \\ G. C. Greubel, Jun 27 2018

Crossrefs

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

Sequence in context: A238780 A330545 A113298 * A218699 A090794 A254858

Adjacent sequences: A058702 A058703 A058704 * A058706 A058707 A058708

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 27 2018

Status

approved