A058691 McKay-Thompson series of class 48A for Monster.

1, 1, 1, 3, 2, 3, 6, 5, 7, 12, 12, 15, 21, 21, 27, 36, 40, 48, 62, 69, 81, 102, 112, 132, 164, 183, 212, 258, 286, 330, 396, 440, 507, 600, 668, 765, 893, 994, 1133, 1311, 1462, 1659, 1906, 2123, 2396, 2736, 3044, 3423, 3893, 4324, 4848, 5487, 6080, 6798, 7660, 8478, 9457, 10614

Offset

-1,4

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^2)*eta(q^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))) in powers of q. - G. C. Greubel, Jun 27 2018

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

Example

T48A = 1/q + q + q^3 + 3*q^5 + 2*q^7 + 3*q^9 + 6*q^11 + 5*q^13 + 7*q^15 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^4]* eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8]*eta[q^24]));  a:= CoefficientList[Series[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^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))); Vec(A) \\ G. C. Greubel, Jun 27 2018

Crossrefs

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

Sequence in context: A033783 A033807 A371070 * A281667 A368102 A336749

Adjacent sequences: A058688 A058689 A058690 * A058692 A058693 A058694

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