A058644 McKay-Thompson series of class 36A for Monster.

1, 0, 3, 2, 3, 6, 10, 12, 15, 22, 30, 36, 44, 60, 78, 96, 117, 150, 190, 228, 276, 340, 420, 504, 603, 732, 885, 1052, 1245, 1488, 1770, 2088, 2454, 2902, 3420, 3996, 4666, 5460, 6378, 7400, 8583, 9972, 11566, 13344, 15378, 17752, 20448, 23472, 26904, 30876

Offset

-1,3

Comments

A058533, A123676, A215412, A058644, A215413, A227585 are all essentially the same sequence. - N. J. A. Sloane, Aug 09 2012

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

a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

Example

T36A = 1/q + 3*q + 2*q^2 + 3*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 15*q^7 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; e36B2:= eta[q]*eta[q^4]*eta[q^18]/( eta[q^2]*eta[q^9]*eta[q^36]); T36A := 1 +e36B2 +3/e36B2; a:= CoefficientList[Series[q*T36A, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 09 2018 *)

Prog

(PARI) q='q+O('q^50); Vec(1 + (eta(q)*eta(q^4)*eta(q^18)/(eta(q^2) *eta(q^9)*eta(q^36)))/q + 3*q*(eta(q^2)*eta(q^9)*eta(q^36)/(eta(q) *eta(q^4)*eta(q^18)))) \\ G. C. Greubel, May 09 2018

Crossrefs

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

Sequence in context: A050062 A058533 A215413 * A049923 A184881 A007054

Adjacent sequences: A058641 A058642 A058643 * A058645 A058646 A058647

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved