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A112223 McKay-Thompson series of class 132a for the Monster group. 1
1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 3, 1, 3, 2, 3, 3, 5, 3, 5, 4, 5, 5, 7, 5, 8, 7, 8, 8, 11, 8, 12, 10, 12, 12, 16, 12, 18, 16, 19, 18, 23, 19, 26, 23, 27, 27, 33, 28, 37, 34, 39, 38, 47, 41, 52, 48, 55, 55, 66, 58, 73, 68, 77, 77, 91, 82, 100, 95, 107, 107, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

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(T66A) in powers of q, where T66A = A058739. - G. C. Greubel, Jul 03 2018

a(n) ~ exp(2*Pi*sqrt(n/33)) / (2 * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 03 2018

EXAMPLE

T132a = 1/q +q^3 +q^9 +q^11 +q^15 +q^17 +q^19 +q^21 +2*q^23 +...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 120; b:= (eta[q^2]*eta[q^3]* eta[q^22]*eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]);  T66A:= -1 + b + 1/b; a:= CoefficientList[Series[(q*T66A + 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^2)*eta(q^3)* eta(q^22)*eta(q^33))/(q* eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); T66A = b - 1 + 1/b; Vec(sqrt(q*T66A)) \\ G. C. Greubel, Jul 03 2018

CROSSREFS

Sequence in context: A026904 A057828 A082498 * A178771 A289498 A193929

Adjacent sequences:  A112220 A112221 A112222 * A112224 A112225 A112226

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 21 17:07 EST 2019. Contains 319350 sequences. (Running on oeis4.)