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A112219 McKay-Thompson series of class 104A for the Monster group. 1
1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 3, 4, 3, 5, 4, 6, 5, 7, 6, 9, 7, 11, 9, 13, 11, 15, 13, 18, 16, 21, 19, 25, 22, 29, 27, 34, 31, 40, 37, 46, 43, 53, 50, 62, 58, 71, 68, 83, 78, 95, 91, 109, 104, 124, 120, 143, 137, 162, 158, 185, 180, 210, 206, 239, 234, 270, 266 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Also McKay-Thompson series of class 104B for Monster. - Michel Marcus, Feb 19 2014

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of sqrt(T52A) in powers of q, where T52A = A058705. - G. C. Greubel, Jul 02 2018

a(n) ~ exp(sqrt(2*n/13)*Pi) / (2^(5/4) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T104A = 1/q +q^7 +q^11 +q^15 +q^23 +q^27 +2*q^31 +q^35 +2*q^39 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= q^(1/2)*(eta[q^2]* eta[q^13]/(eta[q]*eta[q^26])); T52A:= B - q/B; a:= CoefficientList[ Series[(T52A + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 02 2018 *)

PROG

(PARI) q='q+O('q^70); B = (eta(q^2)*eta(q^13)/(eta(q)*eta(q^26))); Vec(sqrt(B - q/B)) \\ G. C. Greubel, Jul 02 2018

CROSSREFS

Sequence in context: A079135 A271315 A212813 * A035458 A259771 A194902

Adjacent sequences:  A112216 A112217 A112218 * A112220 A112221 A112222

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)