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A058689 McKay-Thompson series of class 46C for the Monster group. 1
1, 0, 2, 1, 3, 3, 5, 5, 10, 8, 14, 14, 23, 21, 33, 32, 49, 49, 69, 70, 99, 100, 136, 142, 190, 198, 259, 271, 351, 370, 469, 498, 627, 665, 824, 884, 1084, 1162, 1413, 1518, 1833, 1974, 2360, 2548, 3031, 3272, 3865, 4185, 4917, 5321, 6218, 6739, 7838 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

Also McKay-Thompson series of class 46D for the Monster group.

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 A + 1 + 2/A, where A = eta(q)*eta(q^23)/(eta(q^2)* eta(q^46)), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(2*Pi*sqrt(2*n/23)) / (2^(3/4) * 23^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T46C = 1/q +2*q +q^2 +3*q^3 +3*q^4 +5*q^5 +5*q^6 +10*q^7 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q]*eta[q^23]/( eta[q^2]* eta[q^46])); a:= CoefficientList[Series[1 + A + 2/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)*eta(q^23)/(q*eta(q^2)* eta(q^46)); Vec(A + 1 + 2/A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A070047 A101198 A034394 * A173510 A238785 A241389

Adjacent sequences:  A058686 A058687 A058688 * A058690 A058691 A058692

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)