A112160 McKay-Thompson series of class 24E for the Monster group.

1, 4, 6, 8, 17, 28, 38, 56, 84, 124, 172, 232, 325, 448, 594, 784, 1049, 1388, 1796, 2320, 3005, 3864, 4912, 6216, 7877, 9940, 12430, 15488, 19309, 23972, 29580, 36408, 44766, 54876, 66978, 81536, 99150, 120272, 145374, 175344, 211242

Offset: 0

Author

Michael Somos, Aug 28 2005

Keywords

• nonn

Examples

			T24E = 1/q + 4*q^5 + 6*q^11 + 8*q^17 + 17*q^23 + 28*q^29 + 38*q^35 + ...
		

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

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)
eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/6)*(eta[q^2]^2/(eta[q]*eta[q^4]))^4, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 25 2018 *)

PARI

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

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2 * 6^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 27 2015

Expansion of q^(1/6)*(eta(q^2)^2/(eta(q)*eta(q^4)))^4 in powers of q. - G. C. Greubel, Jan 25 2018

G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - (-x)^k))). - Ilya Gutkovskiy, Jun 07 2018