A112224 - OEIS

A112224

McKay-Thompson series of class 140a for the Monster group.

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

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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: A185317 A373606 A008682 * A058774 A033101 A220413

Adjacent sequences: A112221 A112222 A112223 * A112225 A112226 A112227

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved