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A058707 McKay-Thompson series of class 52a for Monster. 1
1, 2, 0, 2, 1, 4, 3, 6, 5, 10, 8, 14, 13, 20, 19, 28, 26, 40, 39, 54, 54, 76, 75, 100, 103, 136, 138, 180, 183, 236, 245, 308, 320, 402, 417, 516, 541, 664, 696, 844, 890, 1070, 1131, 1350, 1431, 1700, 1802, 2124, 2261, 2648, 2821, 3288, 3507, 4070, 4343, 5014, 5361, 6168, 6593, 7552, 8087 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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 + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^13)/(eta(q)* eta(q^26))), in powers of q. - G. C. Greubel, Jun 27 2018

a(n) ~ exp(2*Pi*sqrt(n/13)) / (2 * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T52a = 1/q + 2*q + 2*q^5 + q^7 + 4*q^9 + 3*q^11 + 6*q^13 + 5*q^15 + 10*q^17 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/( eta[q]*eta[q^26]));  a:= SeriesCoefficient[A + 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^2)*eta(q^13)/(eta(q)*eta(q^26)); Vec(A + q/A) \\ G. C. Greubel, Jun 27 2018

CROSSREFS

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

Sequence in context: A029181 A261426 A260574 * A242691 A081082 A049785

Adjacent sequences:  A058704 A058705 A058706 * A058708 A058709 A058710

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 15 00:14 EDT 2019. Contains 328025 sequences. (Running on oeis4.)