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A112220 McKay-Thompson series of class 117a for the Monster group. 1
1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 4, 3, 4, 5, 4, 6, 6, 6, 7, 8, 7, 9, 10, 10, 11, 13, 12, 15, 16, 16, 18, 21, 19, 23, 25, 25, 28, 31, 30, 35, 38, 38, 42, 47, 46, 52, 56, 57, 62, 69, 68, 77, 82, 84, 91, 100, 100, 111, 118, 121, 131, 142, 144, 158, 168, 173 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..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 (T39A + 3)^(1/3) in powers of q, where T39A = A058659. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(4*Pi*sqrt(n/13)/3) / (sqrt(6) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T117a = 1/q +q^2 +q^11 +q^17 +q^20 +q^23 +q^26 +2*q^29 +q^32 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; c:= (eta[q^3]*eta[q^13]/ (eta[q]*eta[q^39])); T39A := c + 1/c - 1; a:= CoefficientList[Series[ (q*T39A + 3*q + O[q]^nmax)^(1/3), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

PROG

(PARI) seq(n)={my(x=x+O(x*x^n)); my(A=eta(x^3)*eta(x^13)/(x*eta(x)*eta(x^39))); Vec((x*(2 + A + 1/A))^(1/3))} \\ Andrew Howroyd, Jul 02 2018

CROSSREFS

Cf. A058659.

Sequence in context: A025832 A320385 A112222 * A185278 A241065 A086376

Adjacent sequences:  A112217 A112218 A112219 * A112221 A112222 A112223

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 20 04:21 EST 2019. Contains 319323 sequences. (Running on oeis4.)