A058614 McKay-Thompson series of class 30C for Monster.

1, 0, 0, -2, 2, -2, 3, -2, 5, -6, 5, -6, 9, -10, 10, -16, 17, -18, 25, -26, 31, -38, 37, -48, 60, -62, 68, -84, 95, -104, 125, -134, 154, -182, 192, -220, 257, -274, 309, -360, 394, -434, 492, -544, 607, -688, 740, -824, 944, -1018, 1123, -1266, 1377, -1524, 1697, -1850, 2041, -2264, 2461, -2708

Offset

-1,4

Links

Seiichi Manyama, Table of n, a(n) for n = -1..10000

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

G.f.: u + v - 1 = u * v + 1 where u = Product_{k>0} (1 - x^k) * (1 - x^(15*k)) / ((1 - x^(6*k)) * (1 - x^(10*k))), v = 1/x * Product_{k>0} (1 - x^(3*k)) * (1 - x^(5*k)) / ((1 - x^(2*k)) * (1 - x^(30*k))). - Seiichi Manyama, May 04 2017

a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jun 06 2018

Expansion of 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/(eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30)) in powers of q. - G. C. Greubel, Jun 14 2018

Example

T30C = 1/q - 2*q^2 + 2*q^3 - 2*q^4 + 3*q^5 - 2*q^6 + 5*q^7 - 6*q^8 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(1 + eta[q]*eta[q^3]*eta[q^5]*eta[q^15]/(eta[q^2]*eta[q^6]* eta[q^10]* eta[q^30])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
QP=QPochhammer; a:= CoefficientList[Series[q + QP[q]*QP[q^3]*QP[q^5]* QP[q^15]/(QP[q^2]*QP[q^6]*QP[q^10]*QP[q^30]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

Prog

(PARI) q='q+O('q^50); A = 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/( eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30))/q; Vec(A) \\ G. C. Greubel, Jun 14 2018

Crossrefs

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

Cf. A132321 (same sequence except for n=0).

Cf. A131797 (u), A058618 (v).

Sequence in context: A283751 A132321 A058726 * A122765 A131053 A219281

Adjacent sequences: A058611 A058612 A058613 * A058615 A058616 A058617

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved