A112184 McKay-Thompson series of class 44b for the Monster group.

1, -1, 0, -1, 1, -1, 1, -1, 2, -2, 2, -3, 4, -3, 4, -5, 6, -6, 6, -8, 9, -10, 10, -12, 14, -15, 16, -19, 21, -22, 24, -27, 31, -34, 36, -40, 46, -48, 52, -58, 64, -69, 74, -82, 91, -98, 104, -115, 127, -136, 145, -159, 174, -186, 200, -218, 238, -254, 272, -296, 322, -343, 366, -398, 430, -460, 492, -531

Offset

0,9

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 q^(1/2)*(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22))) in powers of q. - G. C. Greubel, Jun 28 2018

a(n) ~ (-1)^n * exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

Example

T44b = 1/q -q -q^5 +q^7 -q^9 +q^11 -q^13 +2*q^15 -2*q^17 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^11]/(eta[q^2]*eta[q^22])), {q, 0, 60}], q];  Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)
nmax = 60; CoefficientList[Series[Product[(1 - x^(2*k-1))*(1 - x^(22*k-11)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 29 2018 *)

Prog

(PARI) q='q+O('q^50); Vec((eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))) \\ G. C. Greubel, Jun 28 2018

Crossrefs

Sequence in context: A060473 A055034 A362739 * A112213 A238957 A238970

Adjacent sequences: A112181 A112182 A112183 * A112185 A112186 A112187

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved