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A058554 McKay-Thompson series of class 20E for Monster. 1
1, 3, 6, 13, 24, 39, 64, 102, 153, 230, 342, 492, 704, 999, 1392, 1922, 2637, 3576, 4812, 6438, 8547, 11278, 14802, 19317, 25078, 32403, 41670, 53358, 68043, 86424, 109378, 137934, 173346, 217166, 271218, 337692, 419287, 519174, 641124, 789744, 970455, 1189659, 1455086, 1775850 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of  q^(1/2)*(eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^3 in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T20E = 1/q + 3*q + 6*q^3 + 13*q^5 + 24*q^7 + 39*q^9 + 64*q^11 + 102*q^13 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)*eta(q^10)))^3; Vec(A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A002799 A285263 A162426 * A128517 A022568 A120006

Adjacent sequences:  A058551 A058552 A058553 * A058555 A058556 A058557

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

STATUS

approved

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Last modified January 22 11:56 EST 2019. Contains 319363 sequences. (Running on oeis4.)