A112220 McKay-Thompson series of class 117a for the Monster group.

1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 4, 3, 4, 5, 4, 6, 6, 6, 7, 8, 7, 9, 10, 10, 11, 13, 12, 15, 16, 16, 18, 21, 19, 23, 25, 25, 28, 31, 30, 35, 38, 38, 42, 47, 46, 52, 56, 57, 62, 69, 68, 77, 82, 84, 91, 100, 100, 111, 118, 121, 131, 142, 144, 158, 168, 173

Offset

0,11

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 (T39A + 3)^(1/3) in powers of q, where T39A = A058659. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(4*Pi*sqrt(n/13)/3) / (sqrt(6) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T117a = 1/q +q^2 +q^11 +q^17 +q^20 +q^23 +q^26 +2*q^29 +q^32 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; c:= (eta[q^3]*eta[q^13]/ (eta[q]*eta[q^39])); T39A := c + 1/c - 1; a:= CoefficientList[Series[ (q*T39A + 3*q + O[q]^nmax)^(1/3), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

Prog

(PARI) seq(n)={my(x=x+O(x*x^n)); my(A=eta(x^3)*eta(x^13)/(x*eta(x)*eta(x^39))); Vec((x*(2 + A + 1/A))^(1/3))} \\ Andrew Howroyd, Jul 02 2018

Crossrefs

Cf. A058659.

Sequence in context: A025832 A320385 A112222 * A185278 A241065 A086376

Adjacent sequences: A112217 A112218 A112219 * A112221 A112222 A112223

Keyword

nonn,changed

Author

Michael Somos, Aug 28 2005

Status

approved