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A058597 McKay-Thompson series of class 26B for Monster. 2
1, 0, 3, 6, 9, 14, 22, 32, 46, 66, 93, 128, 176, 236, 315, 420, 550, 718, 932, 1198, 1534, 1956, 2476, 3120, 3919, 4896, 6095, 7562, 9341, 11504, 14126, 17284, 21090, 25666, 31140, 37692, 45515, 54818, 65878, 79000, 94523, 112872, 134522, 160004 (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

a(n) ~ exp(2*Pi*sqrt(2*n/13)) / (2^(3/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

Expansion of -2 + ((eta(q^2)*eta(q^13))/(eta(q)* eta(q^26)))^2 in powers of q. - G. C. Greubel, Feb 18 2018

EXAMPLE

T26B = 1/q + 3*q + 6*q^2 + 9*q^3 + 14*q^4 + 22*q^5 + 32*q^6 + 46*q^7 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; e26B:= ((eta[q^2]*eta[q^13])/(eta[q]* eta[q^26]))^2; Table[SeriesCoefficient[-2 + e26B, {q, 0, n}], {n, -1, 50}] (* G. C. Greubel, Feb 18 2018 *)

PROG

(PARI) q='q+O('q^50); A = -2 + ((eta(q^2)*eta(q^13))/(eta(q)*eta(q^26)) )^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018

CROSSREFS

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

Cf. A128518 (same sequence except for n=0).

Sequence in context: A083853 A310173 A310174 * A310175 A146562 A179893

Adjacent sequences:  A058594 A058595 A058596 * A058598 A058599 A058600

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 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)