A058660 - OEIS

A058660

McKay-Thompson series of class 39B for Monster.

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: A080013 A152949 A338431 * 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