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A058644 McKay-Thompson series of class 36A for Monster. 6
1, 0, 3, 2, 3, 6, 10, 12, 15, 22, 30, 36, 44, 60, 78, 96, 117, 150, 190, 228, 276, 340, 420, 504, 603, 732, 885, 1052, 1245, 1488, 1770, 2088, 2454, 2902, 3420, 3996, 4666, 5460, 6378, 7400, 8583, 9972, 11566, 13344, 15378, 17752, 20448, 23472, 26904, 30876 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

A058533, A123676, A215412, A058644, A215413, A227585 are all essentially the same sequence. - N. J. A. Sloane, Aug 09 2012

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(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

EXAMPLE

T36A = 1/q + 3*q + 2*q^2 + 3*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 15*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; e36B2:= eta[q]*eta[q^4]*eta[q^18]/( eta[q^2]*eta[q^9]*eta[q^36]); T36A := 1 +e36B2 +3/e36B2; a:= CoefficientList[Series[q*T36A, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 09 2018 *)

PROG

(PARI) q='q+O('q^50); Vec(1 + (eta(q)*eta(q^4)*eta(q^18)/(eta(q^2) *eta(q^9)*eta(q^36)))/q + 3*q*(eta(q^2)*eta(q^9)*eta(q^36)/(eta(q) *eta(q^4)*eta(q^18)))) \\ G. C. Greubel, May 09 2018

CROSSREFS

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

Sequence in context: A050062 A058533 A215413 * A049923 A184881 A007054

Adjacent sequences:  A058641 A058642 A058643 * A058645 A058646 A058647

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 23 03:08 EST 2019. Contains 319370 sequences. (Running on oeis4.)