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A007254 McKay-Thompson series of class 6A for Monster.
(Formerly M5355)
5
1, 0, 79, 352, 1431, 4160, 13015, 31968, 81162, 183680, 412857, 864320, 1805030, 3564864, 7000753, 13243392, 24805035, 45168896, 81544240, 143832672, 251550676, 432030080, 735553575, 1233715328, 2052941733 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
a(n) = A121665(n) + A226235(n) = A121666(n) + 64*A123653(n) = A121667(n) + 81*A284607(n) for n > 0. - Seiichi Manyama, Mar 30 2017
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 30 2017
EXAMPLE
T6A = 1/q + 79*q + 352*q^2 + 1431*q^3 + 4160*q^4 + 13015*q^5 + 31968*q^6 + ...
MATHEMATICA
nmax = 50; Flatten[{1, 0, Rest[Rest[CoefficientList[Series[Product[((1 + x^k)/(1 + x^(3*k)))^12, {k, 1, nmax}] + x^2*Product[((1 + x^(3*k))/(1 + x^k))^12, {k, 1, nmax}], {x, 0, nmax}], x]]]}] (* Vaclav Kotesovec, Mar 30 2017 *)
eta[q_] := q^(1/24)*QPochhammer[q]; e6B:= (eta[q^2]*eta[q^3]/(eta[q]* eta[q^6]))^12; a:= CoefficientList[Series[q*(e6B - 12 + 1/e6B), {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (*G. C. Greubel, May 10 2018 *)
PROG
(PARI) q='q+O('q^50); F =(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(F -12 +1/F) \\ G. C. Greubel, May 10 2018
CROSSREFS
Cf. A045484.
Sequence in context: A157507 A142897 A142330 * A142439 A200847 A132252
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)