A112173 McKay-Thompson series of class 36b for the Monster group.

1, 2, 1, 4, 8, 6, 10, 16, 18, 26, 33, 40, 58, 74, 82, 112, 147, 166, 212, 268, 316, 392, 476, 560, 695, 838, 967, 1184, 1430, 1648, 1970, 2352, 2731, 3236, 3803, 4404, 5206, 6080, 6984, 8192, 9553, 10942, 12709, 14736, 16886, 19506, 22448, 25648

Offset: 0

Author

Michael Somos, Aug 28 2005

Keywords

• nonn

Comments

Convolution square of A112206. - Vaclav Kotesovec, Sep 08 2015

Examples

			T36b = 1/q +2*q^2 +q^5 +4*q^8 +8*q^11 +6*q^14 +10*q^17 +...
		

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).
• Index entries for McKay-Thompson series for Monster simple group

Crossrefs

Cf. A112206.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Product[((1 + x^k)*(1 + x^(3*k)) / ((1 + x^(2*k))*(1 + x^(6*k))))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)
eta[q_]:= q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q^(1/3)*((eta[q^2]*eta[q^6])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^12]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)

PARI

q='q+O('q^50); A = ((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)* eta(q^4)*eta(q^12)))^2; Vec(A) \\ G. C. Greubel, Jun 16 2018

Formula

a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2015

Expansion of q^(1/3)*((eta(q^2)*eta(q^6))^2/(eta(q)*eta(q^3)*eta(q^4)* eta(q^12)))^2 in powers of q. - G. C. Greubel, Jun 16 2018

Expansion of abs(q^(1/3)*(eta(q)*eta(q^3)/(eta(q^2)*eta(q^6)))^2) in powers of q. - G. C. Greubel, Jun 16 2018