A058549 McKay-Thompson series of class 19A for Monster.

1, 0, 6, 10, 21, 36, 61, 96, 156, 232, 357, 522, 768, 1092, 1563, 2174, 3039, 4164, 5695, 7686, 10362, 13792, 18333, 24138, 31706, 41316, 53712, 69348, 89319, 114396, 146114, 185724, 235482, 297252, 374316, 469578, 587646, 732888, 911961, 1131250

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..5000

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(4*Pi*sqrt(n/19)) / (sqrt(2)*19^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

G.f.: - 3 + (1/x) * ( G(x) * G(x^19) + x^4 * H(x) * H(x^19) )^3 where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 25 2018

Example

T19A = 1/q + 6*q + 10*q^2 + 21*q^3 + 36*q^4 + 61*q^5 + 96*q^6 + 156*q^7 + ...

Mathematica

QP = QPochhammer; G[x_]:= 1/(QP[x, x^5]*QP[x^4, x^5]); H[x_]:= 1/(QP[x^2, x^5]*QP[x^3, x^5]); a:= CoefficientList[Series[-3 *x + (G[x]*G[x^19] + x^4*H[x]*H[x^19])^3, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)

Prog

(PARI) q='q+O('q^40);  A = (eta(q)*eta(q^19)/(eta(q^2)*eta(q^38)))^2; B = - (eta(-q)*eta(-q^19)/(eta(q^2)*eta(q^38)))^2; F = (q^4/(A*B) - (A + B)/(4*q))^3; v=Vec(F-3*q^2); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jun 25 2018

Crossrefs

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

Cf. A136569 (same sequence except for n=0).

Sequence in context: A030007 A323729 A372295 * A363675 A271511 A287993

Adjacent sequences: A058546 A058547 A058548 * A058550 A058551 A058552

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved