A058707 McKay-Thompson series of class 52a for Monster.

1, 2, 0, 2, 1, 4, 3, 6, 5, 10, 8, 14, 13, 20, 19, 28, 26, 40, 39, 54, 54, 76, 75, 100, 103, 136, 138, 180, 183, 236, 245, 308, 320, 402, 417, 516, 541, 664, 696, 844, 890, 1070, 1131, 1350, 1431, 1700, 1802, 2124, 2261, 2648, 2821, 3288, 3507, 4070, 4343, 5014, 5361, 6168, 6593, 7552, 8087

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 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 + 2*q^5 + q^7 + 4*q^9 + 3*q^11 + 6*q^13 + 5*q^15 + 10*q^17 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/( eta[q]*eta[q^26]));  a:= SeriesCoefficient[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 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: A029181 A261426 A260574 * A242691 A081082 A049785

Adjacent sequences: A058704 A058705 A058706 * A058708 A058709 A058710

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