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A058617 McKay-Thompson series of class 30F for Monster. 2
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 (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

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 A238623 A138135

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

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)