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A058683 McKay-Thompson series of class 44c for Monster. 1
1, 1, 2, 1, 5, 3, 7, 7, 12, 10, 18, 17, 30, 29, 42, 43, 64, 64, 90, 94, 129, 134, 182, 192, 254, 267, 348, 369, 475, 506, 638, 685, 855, 918, 1138, 1226, 1500, 1624, 1964, 2130, 2564, 2781, 3318, 3610, 4283, 4660, 5496, 5983, 7023, 7650, 8925, 9733, 11310, 12330, 14260, 15562, 17932 (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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of A + 2*q/A, where A = q^(1/2)*eta(q)*eta(q^11)/(eta(q^2)* eta(q^22)), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(2*Pi*sqrt(n/11)) / (2 * 11^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T44c = 1/q + q + 2*q^3 + q^5 + 5*q^7 + 3*q^9 + 7*q^11 + 7*q^13 + 12*q^15 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^11]/( eta[q^2]*eta[q^22])); a:= CoefficientList[Series[A + 2*q/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^11)/(eta(q^2)*eta(q^22)); Vec(A + 2*q/A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A127367 A054084 A296069 * A286295 A026205 A082748

Adjacent sequences:  A058680 A058681 A058682 * A058684 A058685 A058686

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 October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)