A112196 McKay-Thompson series of class 56a for the Monster group.

1, 1, 1, 1, 3, 2, 2, 5, 6, 7, 7, 9, 12, 13, 16, 20, 25, 27, 31, 38, 44, 51, 58, 69, 80, 92, 102, 118, 141, 157, 177, 203, 234, 261, 292, 336, 382, 428, 475, 540, 610, 677, 757, 852, 957, 1060, 1179, 1318, 1470, 1634, 1806, 2011, 2236, 2469, 2724, 3020, 3350

Offset

0,5

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(T28B + 2) in powers of q, where T28B = A112169. - G. C. Greubel, Jul 01 2018

a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

Example

T56a = 1/q +q +q^3 +q^5 +3*q^7 +2*q^9 +2*q^11 +5*q^13 +6*q^15 +...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 70; A:= (eta[q]*eta[q^7]/ (eta[q^4]*eta[q^28])); T28B := 1 + A + 4/A; a:= CoefficientList[Series[ (q*(T28B + 2) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q)*eta(q^7)/(q*eta(q^4)*eta(q^28)); T28B = A + 1 + 4/A; Vec(sqrt(q*(T28B + 2))) \\ G. C. Greubel, Jul 01 2018

Crossrefs

Cf. A112169.

Sequence in context: A205675 A342331 A058608 * A021035 A259967 A007567

Adjacent sequences: A112193 A112194 A112195 * A112197 A112198 A112199

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved