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A058641 McKay-Thompson series of class 35B for Monster. 2
1, 0, 2, 3, 5, 6, 10, 12, 18, 23, 31, 39, 54, 66, 86, 107, 137, 168, 213, 259, 323, 392, 482, 580, 711, 850, 1029, 1228, 1476, 1750, 2093, 2470, 2934, 3453, 4078, 4780, 5625, 6566, 7689, 8952, 10440, 12113, 14080, 16286, 18865, 21764, 25127, 28910, 33289 (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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -1 + (eta(q^5)*eta(q^7))/(eta(q)*eta(q^35)) in powers of q. - G. C. Greubel, Jan 28 2018

a(n) ~ exp(4*Pi*sqrt(n/35)) / (sqrt(2) * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018

EXAMPLE

T35B = 1/q + 2*q + 3*q^2 + 5*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 18*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[-1 + (eta[q^5]*eta[q^7])/(eta[q]*eta[q^35]), {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 28 2018)

PROG

(PARI) q='q+O('q^50); A = -1 + (eta(q^5)*eta(q^7))/(eta(q)*eta(q^35))/q; Vec(A) \\ G. C. Greubel, Jun 14 2018

CROSSREFS

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

Cf. A212253 (same sequence except for n=0).

Sequence in context: A304405 A097071 A105420 * A212253 A237831 A241829

Adjacent sequences:  A058638 A058639 A058640 * A058642 A058643 A058644

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 18 2014

STATUS

approved

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)