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A058637 McKay-Thompson series of class 33B for Monster. 2
1, 0, 2, 4, 5, 6, 14, 14, 20, 30, 37, 46, 71, 82, 108, 144, 173, 218, 291, 340, 425, 540, 647, 788, 996, 1170, 1427, 1744, 2072, 2476, 3019, 3536, 4224, 5058, 5942, 7008, 8363, 9734, 11453, 13512, 15719, 18340, 21546, 24908, 28983, 33774, 38995, 45086, 52353 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
Expansion of A + 1 + 3/A, where A =eta(q)*eta(q^11)/(eta(q^3)*eta(q^33)), in powers of q. - G. C. Greubel, Jun 23 2018
a(n) ~ exp(4*Pi*sqrt(n/33)) / (sqrt(2) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T33B = 1/q + 2*q + 4*q^2 + 5*q^3 + 6*q^4 + 14*q^5 + 14*q^6 + 20*q^7 + ...
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; A := eta[q]*eta[q^11]/( eta[q^3]* eta[q^33]); a:= CoefficientList[Series[q*(A + 1 + 3/A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)
PROG
(PARI) q='q+O('q^50); A = eta(q)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(A + 1 + 3/A) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
Sequence in context: A191165 A360994 A324778 * A026473 A272929 A336129
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 20 2014
STATUS
approved

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Last modified March 19 02:55 EDT 2024. Contains 370952 sequences. (Running on oeis4.)