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A058551 McKay-Thompson series of class 20B for Monster. 1
1, 2, 9, 10, 28, 30, 73, 96, 165, 212, 358, 468, 746, 950, 1449, 1844, 2727, 3480, 4935, 6288, 8715, 11056, 15091, 18990, 25468, 31910, 42225, 52752, 68785, 85536, 110371, 136744, 174816, 215480, 273152, 335388, 421909, 516244, 644550, 785784, 974921, 1184430, 1461239, 1768900 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 + 4*q/A, where A = q^(1/2)*(eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2, in powers of q. - G. C. Greubel, Jun 21 2018

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T20B = 1/q + 2*q + 9*q^3 + 10*q^5 + 28*q^7 + 30*q^9 + 73*q^11 + 96*q^13 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]*eta[q^5]/(eta[q^2] *eta[q^10]))^2; a:= CoefficientList[Series[A + 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 21 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q)*eta(q^5)/(eta(q^2) *eta(q^10)))^2; Vec(A + 4*q/A) \\ G. C. Greubel, Jun 21 2018

CROSSREFS

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

Sequence in context: A081346 A301872 A290592 * A119183 A179888 A073082

Adjacent sequences:  A058548 A058549 A058550 * A058552 A058553 A058554

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

STATUS

approved

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Last modified January 17 10:21 EST 2019. Contains 319218 sequences. (Running on oeis4.)