A058206 McKay-Thompson series of class 12C for the Monster group.

1, 7, 15, 71, 106, 273, 486, 961, 1563, 3040, 4692, 8199, 12773, 20919, 31569, 50552, 74368, 114504, 167366, 250033, 358845, 527650, 745688, 1073784, 1504452, 2129317, 2947224, 4122518, 5644462, 7792122, 10585876, 14446420, 19450323, 26307536, 35131220, 47077341, 62449405, 82987854, 109317927, 144252191

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..128 from G. A. Edgar)

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Michael Somos, Emails to N. J. A. Sloane, 1993

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of q^(1/2)*(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^6 + (eta(q)*eta(q^6)/(eta(q^2)*eta(q^3)))^6 in powers of q. - G. A. Edgar, Mar 13 2017

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 18 2017

G.f. is a period 1 Fourier series which satisfies f(-1 / (24 t)) = f(t) where q = exp(2 Pi i t). - Michael Somos, Jul 06 2018

Example

T12C = 1/q + 7*q + 15*q^3 + 71*q^5 + 106*q^7 + 273*q^9 + 486*q^11 + ...

Mathematica

QP := QPochhammer; CoefficientList[Series[QP[x^2]^6*QP[x^3]^6 / (QP[x]^6*QP[x^6]^6) + x*QP[x]^6*QP[x^6]^6 / (QP[x^2]^6*QP[x^3]^6), {x, 0, 66}], x] (* Indranil Ghosh, Mar 14 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]* eta[q^3]/( eta[q]*eta[q^6]))^6; a := CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)
a[ n_] := With[{A = (QPochhammer[ x^3, x^6] / QPochhammer[ x, x^2])^6 },
SeriesCoefficient[ A + x / A, {x, 0, n}]]; (* Michael Somos, Jul 06 2018 )

Prog

(PARI) q='q+O('q^66); Vec( eta(q^2)^6*eta(q^3)^6 / (eta(q)^6*eta(q^6)^6) + q* eta(q)^6*eta(q^6)^6 / (eta(q^2)^6*eta(q^3)^6) )  \\ Joerg Arndt, Mar 13 2017

Crossrefs

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

Sequence in context: A279882 A171064 A042313 * A219523 A177128 A177177

Adjacent sequences: A058203 A058204 A058205 * A058207 A058208 A058209

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from G. A. Edgar, Mar 13 2017

Status

approved