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A058675 McKay-Thompson series of class 42a for Monster. 2
1, 0, 3, 3, 3, 6, 7, 6, 12, 16, 18, 24, 33, 33, 48, 57, 69, 87, 106, 117, 153, 181, 207, 258, 307, 345, 429, 496, 570, 681, 805, 906, 1083, 1252, 1425, 1671, 1934, 2190, 2562, 2929, 3327, 3840, 4400, 4953, 5727, 6500, 7335, 8388, 9521, 10686, 12198, 13775 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 30 2018
Expansion of A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))), in powers of q. - G. C. Greubel, Jun 19 2018
EXAMPLE
T42a = 1/q + 3*q^3 + 3*q^5 + 3*q^7 + 6*q^9 + 7*q^11 + 6*q^13 + 12*q^15 + ...
MATHEMATICA
CoefficientList[Series[(QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]), {x, 0, 100}], x] (* Vaclav Kotesovec, May 30 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^7]/( eta[q]*eta[q^21])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))); Vec(A - q/A) \\ G. C. Greubel, Jun 19 2018
CROSSREFS
Sequence in context: A219299 A219595 A219173 * A025497 A031502 A153004
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Vaclav Kotesovec, May 30 2018
STATUS
approved

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Last modified February 21 16:42 EST 2024. Contains 370237 sequences. (Running on oeis4.)