A058744 McKay-Thompson series of class 70A for Monster.

1, 0, 1, 0, 2, 2, 2, 2, 3, 2, 4, 4, 7, 4, 10, 8, 11, 10, 14, 14, 21, 18, 25, 22, 33, 32, 41, 38, 52, 50, 65, 62, 82, 78, 101, 102, 124, 122, 150, 152, 189, 186, 230, 226, 279, 280, 334, 340, 402, 412, 487, 492, 582, 592, 697, 714, 831, 850, 980, 1014, 1173

Offset

-1,5

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of B + 1 + 1/B, where B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)), in powers of q. - G. C. Greubel, Jun 30 2018

a(n) ~ exp(2*Pi*sqrt(2*n/35)) / (2^(3/4) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 30 2018

Example

T70A = 1/q + q + 2*q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 2*q^8 + 4*q^9 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 30 2018 *)

Prog

(PARI) q='q+O('q^50); B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (q*eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(B + 1 + 1/B) \\ G. C. Greubel, Jun 30 2018

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A029348 A070093 A174931 * A366297 A323246 A364721

Adjacent sequences: A058741 A058742 A058743 * A058745 A058746 A058747

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved