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A058579 McKay-Thompson series of class 24I for Monster. 2
1, 0, 4, 6, 11, 18, 28, 42, 62, 90, 128, 180, 250, 342, 464, 624, 831, 1098, 1440, 1878, 2432, 3132, 4012, 5112, 6485, 8190, 10300, 12900, 16097, 20016, 24804, 30636, 37724, 46314, 56700, 69228, 84302, 102402, 124088, 150024, 180973, 217836 (list; graph; refs; listen; history; text; internal format)
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

Expansion of -1 + (eta(q^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2*eta(q^3) *eta(q^8)*eta(q^12)^2*eta(q^24)) in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T24I = 1/q + 4*q + 6*q^2 + 11*q^3 + 18*q^4 + 28*q^5 + 42*q^6 + 62*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^4]^4*eta[q^6]^4)/(eta[q]* eta[q^2]^2*eta[q^3]*eta[q^8]*eta[q^12]^2*eta[q^24]); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = -1 + (eta(q^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2 *eta(q^3)*eta(q^8)*eta(q^12)^2*eta(q^24))/q; Vec(A) \\ G. C. Greubel, Jun 18 2018

CROSSREFS

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

Cf. A138688 (same sequence except for n=0).

Sequence in context: A296468 A060577 A197985 * A022318 A291916 A047811

Adjacent sequences:  A058576 A058577 A058578 * A058580 A058581 A058582

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 17 19:58 EST 2019. Contains 319251 sequences. (Running on oeis4.)