A058684 McKay-Thompson series of class 45A for Monster.

1, 0, 2, 1, 3, 4, 5, 6, 7, 11, 15, 17, 22, 24, 34, 40, 48, 56, 69, 84, 104, 118, 144, 164, 200, 234, 273, 318, 372, 436, 511, 582, 681, 775, 906, 1036, 1192, 1362, 1562, 1784, 2046, 2315, 2647, 2988, 3409, 3860, 4371, 4936, 5573, 6288, 7104, 7967, 8979, 10052

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5)*eta(q^9)* eta(q^45)) in powers of q. - G. C. Greubel, Jun 19 2018

a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4) * sqrt(6) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

Example

T45A = 1/q + 2*q + q^2 + 3*q^3 + 4*q^4 + 5*q^5 + 6*q^6 + 7*q^7 + 11*q^8 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^15])^2/(eta[q] *eta[q^5]*eta[q^9]*eta[q^45]); a:= CoefficientList[Series[-1 + e45A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); A = -1 + (eta(q^3)*eta(q^15))^2/(eta(q)*eta(q^5) *eta(q^9)*eta(q^45))/q; Vec(A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

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

Cf. A226054 (same sequence except for n=0).

Sequence in context: A375326 A273863 A273864 * A226054 A109920 A109919

Adjacent sequences: A058681 A058682 A058683 * A058685 A058686 A058687

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved