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A058691 McKay-Thompson series of class 48A for Monster. 1
1, 1, 1, 3, 2, 3, 6, 5, 7, 12, 12, 15, 21, 21, 27, 36, 40, 48, 62, 69, 81, 102, 112, 132, 164, 183, 212, 258, 286, 330, 396, 440, 507, 600, 668, 765, 893, 994, 1133, 1311, 1462, 1659, 1906, 2123, 2396, 2736, 3044, 3423, 3893, 4324, 4848, 5487, 6080, 6798, 7660, 8478, 9457, 10614 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,4

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, 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^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))) in powers of q. - G. C. Greubel, Jun 27 2018

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

EXAMPLE

T48A = 1/q + q + q^3 + 3*q^5 + 2*q^7 + 3*q^9 + 6*q^11 + 5*q^13 + 7*q^15 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^4]* eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8]*eta[q^24]));  a:= CoefficientList[Series[A, {q, 0, 60}], q];  Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^4)* eta(q^6)*eta(q^12)/(eta(q)* eta(q^3)*eta(q^8)*eta(q^24))); Vec(A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A222403 A033783 A033807 * A281667 A214297 A022472

Adjacent sequences:  A058688 A058689 A058690 * A058692 A058693 A058694

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 27 2018

STATUS

approved

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Last modified January 22 12:13 EST 2019. Contains 319363 sequences. (Running on oeis4.)