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A058705 McKay-Thompson series of class 52A for Monster. 2
1, 0, 2, 2, 3, 2, 5, 4, 7, 6, 12, 10, 17, 14, 23, 24, 34, 32, 47, 46, 64, 64, 87, 88, 117, 118, 156, 160, 207, 212, 271, 280, 352, 366, 455, 476, 587, 612, 748, 788, 950, 1004, 1205, 1274, 1515, 1608, 1900, 2020, 2373, 2524, 2951, 3148, 3659, 3902, 4521, 4830, 5563, 5948, 6827, 7306, 8353 (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 - 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^3 + 2*q^5 + 3*q^7 + 2*q^9 + 5*q^11 + 4*q^13 + 7*q^15 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/(eta[q]*eta[q^26])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 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: A219606 A238780 A113298 * A218699 A090794 A254858

Adjacent sequences:  A058702 A058703 A058704 * A058706 A058707 A058708

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 19 16:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)