A112185 McKay-Thompson series of class 45c for the Monster group.

1, -1, 0, 1, 1, 1, 0, 0, 1, 0, 1, -1, 0, 1, 1, 2, -2, 0, 1, 1, 3, -1, 0, 2, 1, 3, -2, 0, 2, 1, 5, -4, 0, 4, 3, 6, -3, 0, 4, 2, 7, -5, 0, 5, 4, 10, -7, 0, 7, 5, 12, -7, 0, 9, 5, 14, -9, 0, 10, 6, 20, -14, 0, 14, 10, 23, -13, 0, 16, 9, 27, -18, 0, 19, 13, 35, -24, 0, 24, 16, 42, -25, 0, 29, 18, 48, -31, 0, 33

Offset

0,16

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 (T15b - 3)^(1/3), where T15b = A058513. - G. C. Greubel, Jun 30 2018

Example

T45c = 1/q - q^2 + q^8 + q^11 + q^14 + q^23 + q^29 - q^32 + q^38 + q^41 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]); d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= 2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3; a:= CoefficientList[ Series[(q*(T15b - 3) + O[q]^nmax)^(1/3), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jun 30 2018, fixed by Vaclav Kotesovec, Jul 03 2018 *)

Crossrefs

Sequence in context: A262163 A293112 A306910 * A192062 A172371 A279006

Adjacent sequences: A112182 A112183 A112184 * A112186 A112187 A112188

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved