A058617 McKay-Thompson series of class 30F for Monster.

1, 0, 3, 3, 8, 8, 16, 17, 33, 35, 59, 65, 105, 116, 175, 198, 292, 330, 466, 533, 736, 842, 1132, 1304, 1725, 1985, 2576, 2974, 3809, 4394, 5555, 6415, 8030, 9261, 11475, 13234, 16264, 18734, 22843, 26296, 31849, 36613, 44058, 50602, 60551, 69452, 82669

Offset

-1,3

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).

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

Expansion of -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/(eta(q)* eta(q^2)*eta(q^15)*eta(q^30))) in powers of q. - G. C. Greubel, Jun 18 2018

Example

T30F = 1/q + 3*q + 3*q^2 + 8*q^3 + 8*q^4 + 16*q^5 + 17*q^6 + 33*q^7 + ...

Mathematica

nmax = 50; CoefficientList[Series[-x + Product[(1 - x^(3*k))*(1 - x^(5*k))*(1 - x^(6*k))*(1 - x^(10*k))/((1 - x^k)*(1 - x^(2*k))*(1 - x^(15*k))*(1 - x^(30*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^3]*eta[q^5]*eta[q^6] *eta[q^10])/(eta[q]*eta[q^2]*eta[q^15]*eta[q^30])); a:= CoefficientList[Series[-1 + A, {q, 0, 60}], q];  Table[A058617[n], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Prog

(PARI) q='q+O('q^50); A = -1 + ((eta(q^3)*eta(q^5)*eta(q^6)*eta(q^10))/( eta(q)*eta(q^2)*eta(q^15)*eta(q^30)))/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

Crossrefs

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

Cf. A205977 (same sequence except for n=0).

Sequence in context: A204136 A168283 A135291 * A205977 A363725 A238623

Adjacent sequences: A058614 A058615 A058616 * A058618 A058619 A058620

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved