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A112224 McKay-Thompson series of class 140a for the Monster group. 1
1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 3, 5, 4, 5, 5, 6, 5, 8, 6, 9, 6, 9, 8, 11, 10, 12, 11, 14, 12, 16, 13, 18, 16, 20, 18, 22, 20, 25, 23, 29, 25, 31, 29, 36, 33, 39, 36, 45, 40, 49, 45, 54, 51, 61, 58, 66, 63, 75, 70, 84, 77, 91, 86, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,15

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 sqrt(T70A + 2) in powers of q, where T70A = A058744. - G. C. Greubel, Jul 03 2018

a(n) ~ exp(2*Pi*sqrt(n/35)) / (2 * 35^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 03 2018

EXAMPLE

T140a = 1/q +q +q^7 +q^11 +q^15 +q^19 +q^21 +q^23 +q^25 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 130; b:= eta[q]*eta[q^10]* eta[q^14]*eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); T70A:= 1 + b + 1/b; a:= CoefficientList[Series[(q*T70A + 2*q + O[q]^nmax)^(1/2), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jul 03 2018 *)

PROG

(PARI) q='q+O('q^80); b = eta(q)*eta(q^10)* eta(q^14)*eta(q^35)/(q* eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); T70A = b + 1 + 1/b; Vec(sqrt(q*( T70A + 2))) \\ G. C. Greubel, Jul 03 2018

CROSSREFS

Sequence in context: A287476 A185317 A008682 * A058774 A033101 A220413

Adjacent sequences:  A112221 A112222 A112223 * A112225 A112226 A112227

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 23 03:04 EST 2019. Contains 319368 sequences. (Running on oeis4.)