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

0,2

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A083166 A185292 A022599 * A132040 A210459 A346868

Adjacent sequences: A112157 A112158 A112159 * A112161 A112162 A112163

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved