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A058549 McKay-Thompson series of class 19A for Monster. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A178661 A190273 A030007 * A271511 A287993 A220035

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

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)