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A058660 McKay-Thompson series of class 39B for Monster. 1
1, 1, 3, 3, 4, 6, 10, 10, 16, 19, 26, 31, 41, 50, 65, 80, 99, 119, 150, 178, 219, 262, 317, 376, 453, 534, 642, 754, 896, 1048, 1239, 1444, 1699, 1973, 2308, 2673, 3114, 3592, 4168, 4800, 5544, 6370, 7334, 8395, 9640, 11014, 12601, 14364, 16394, 18638, 21221, 24078, 27344, 30964 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1500

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 (T13A + 3)^(1/3), where T13A = A034319, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T39B = 1/q + q^2 + 3*q^5 + 3*q^8 + 4*q^11 + 6*q^14 + 10*q^17 + 10*q^20 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q];  nmax = 100; T13A := 2 + (eta[q]/ eta[q^13])^2 + 13*(eta[q^13]/eta[q])^2;  a:= CoefficientList[Series[ (q*(T13A + 3) + O[q]^nmax)^(1/3), {q, 0, 70}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

CROSSREFS

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

Sequence in context: A241050 A080013 A152949 * A059871 A273096 A076619

Adjacent sequences:  A058657 A058658 A058659 * A058661 A058662 A058663

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(8) onward added by G. C. Greubel, Jun 24 2018

STATUS

approved

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Last modified January 21 17:47 EST 2019. Contains 319349 sequences. (Running on oeis4.)