A112200 McKay-Thompson series of class 60a for the Monster group.

1, 0, 0, -1, 1, -1, 1, 0, 1, -1, 1, -1, 2, -2, 1, -3, 2, -2, 3, -3, 4, -4, 3, -4, 6, -5, 5, -7, 7, -7, 9, -8, 9, -11, 10, -12, 14, -13, 14, -17, 18, -18, 20, -21, 23, -27, 25, -27, 33, -32, 34, -39, 39, -42, 46, -48, 51, -56, 57, -61, 71, -69, 72, -83, 85, -90, 97, -99, 108, -117, 119, -126, 140, -143, 149, -167, 170

Offset

0,13

Links

G. C. Greubel, Table of n, a(n) for n = 0..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 sqrt(T30C), where T30C = A058614, in powers of q. - G. C. Greubel, Jun 28 2018

a(n) ~ (-1)^n * exp(sqrt(2*n/15)*Pi) / (2^(5/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T60a = 1/q -q^5 +q^7 -q^9 +q^11 +q^15 -q^17 +q^19 -q^21 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= eta[q]*eta[q^3] *eta[q^5]*eta[q^15]/(eta[q^2]*eta[q^6]*eta[q^10]*eta[q^30]); a:= CoefficientList[Series[(q*(1 + A) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)

Prog

(PARI) q='q+O('q^70); A = eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/(q*eta(q^2) *eta(q^6)*eta(q^10)*eta(q^30)); Vec(sqrt(q*(1 + A))) \\ G. C. Greubel, Jul 02 2018

Crossrefs

Sequence in context: A347627 A263107 A286528 * A112221 A266697 A264402

Adjacent sequences: A112197 A112198 A112199 * A112201 A112202 A112203

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved