A058640 McKay-Thompson series of class 35A for Monster.

1, 0, 1, 4, 6, 6, 10, 10, 19, 22, 32, 40, 51, 68, 86, 108, 135, 166, 218, 258, 325, 390, 477, 582, 713, 856, 1025, 1222, 1480, 1750, 2093, 2470, 2930, 3458, 4081, 4782, 5620, 6550, 7702, 8960, 10441, 12110, 14062, 16298, 18863, 21776, 25130, 28884, 33310

Offset

-1,4

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 A - 1 - 1/A, where A = eta(q^5)*eta(q^7)/(eta(q)*eta(q^35)), in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(4*Pi*sqrt(n/35)) / (sqrt(2) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T35A = 1/q + q + 4*q^2 + 6*q^3 + 6*q^4 + 10*q^5 + 10*q^6 + 19*q^7 + 22*q^8 + ...

Mathematica

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

Prog

(PARI) q='q+O('q^50); A = eta(q^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(A - 1 - 1/A) \\ G. C. Greubel, Jun 24 2018

Crossrefs

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

Sequence in context: A098350 A276269 A163173 * A075653 A075656 A267573

Adjacent sequences: A058637 A058638 A058639 * A058641 A058642 A058643

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 20 2014

Status

approved