A058758 McKay-Thompson series of class 84A for Monster.

1, 0, 1, 1, 1, 0, 3, 2, 2, 2, 2, 2, 5, 3, 6, 5, 7, 5, 10, 7, 11, 11, 13, 12, 19, 15, 21, 22, 26, 23, 35, 30, 39, 38, 47, 45, 60, 54, 68, 69, 81, 78, 104, 95, 117, 118, 137, 134, 171, 162, 192, 197, 225, 223, 274, 265, 313, 318, 363, 363, 434, 424, 494, 508, 570, 575, 675, 670, 765, 789, 884

Offset

-1,7

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 B + q/B, where B = q^(1/2)*(eta(q)*eta(q^6)*eta(q^14)* eta(q^21)/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42))), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(n/21)) / (2 * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T84A = 1/q + q^3 + q^5 + q^7 + 3*q^11 + 2*q^13 + 2*q^15 + 2*q^17 + 2*q^19 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; B:= q^(1/2)*(eta[q]*eta[q^6]* eta[q^14]*eta[q^21]/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42])); a:= CoefficientList[Series[B + q/B , {q, 0, 60}], q];  Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 30 2018 *)

Prog

(PARI) q='q+O('q^50); B = (eta(q)*eta(q^6)*eta(q^14)*eta(q^21)/( eta(q^2) *eta(q^3)*eta(q^7)*eta(q^42))); Vec(B + q/B) \\ G. C. Greubel, Jun 30 2018

Crossrefs

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

Sequence in context: A119704 A104223 A057934 * A122396 A272893 A037199

Adjacent sequences: A058755 A058756 A058757 * A058759 A058760 A058761

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 30 2018

Status

approved