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A058598 McKay-Thompson series of class 26a for Monster. 1
1, 2, 4, 6, 13, 16, 27, 38, 57, 78, 112, 146, 205, 272, 367, 476, 634, 816, 1059, 1354, 1738, 2196, 2791, 3492, 4387, 5460, 6798, 8396, 10383, 12740, 15645, 19084, 23288, 28262, 34297, 41412, 49985, 60088, 72184, 86404, 103354, 123214, 146779, 174354, 206895, 244900, 289606, 341660, 402685 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

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 (6 + f)^(1/2), where f = A034318, in powers of q. - G. C. Greubel, Jun 22 2018

a(n) ~ exp(2*Pi*sqrt(2*n/13)) / (2^(3/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T26a = 1/q + 2*q + 4*q^3 + 6*q^5 + 13*q^7 + 16*q^9 + 27*q^11 + 38*q^13 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax := 130; A:= (eta[q]/eta[q^13])^2;

f := A + 13/A; a:= CoefficientList[Series[(q*(6 + f) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 22 2018 *)

CROSSREFS

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

Sequence in context: A307617 A325278 A110980 * A319110 A278031 A087549

Adjacent sequences:  A058595 A058596 A058597 * A058599 A058600 A058601

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 22 2018

STATUS

approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)