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A058608 McKay-Thompson series of class 28C for Monster. 2
1, -1, 1, -1, 3, -2, 2, -5, 6, -7, 7, -9, 12, -13, 16, -20, 25, -27, 31, -38, 44, -51, 58, -69, 80, -92, 102, -118, 141, -157, 177, -203, 234, -261, 292, -336, 382, -428, 475, -540, 610, -677, 757, -852, 957, -1060, 1179, -1318, 1470, -1634, 1806, -2011, 2236, -2469, 2724, -3020, 3350 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

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 (T14B - 2)^(1/2), where T14B = A058503, in powers of q. - G. C. Greubel, Jun 18 2018

a(n) ~ -(-1)^n * exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T28C = 1/q - q + q^3 - q^5 + 3*q^7 - 2*q^9 + 2*q^11 - 5*q^13 + 6*q^15 - ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 100; e28C2:= (eta[q^2]* eta[q^14])^3/(eta[q]*eta[q^4]^2*eta[q^7]*eta[q^28]^2); T14B := -1 + e28C2 + 4/e28C2; a:= CoefficientList[Series[((q (T14B - 2) + O[q]^nmax // Normal /. {q -> q^2}) + O[q]^nmax)^(1/2) // Normal, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

CROSSREFS

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

Sequence in context: A210956 A282161 A205675 * A112196 A021035 A259967

Adjacent sequences:  A058605 A058606 A058607 * A058609 A058610 A058611

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 18 2018

STATUS

approved

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Last modified January 18 16:40 EST 2019. Contains 319271 sequences. (Running on oeis4.)