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A007265 McKay-Thompson series of class 8A for Monster.
(Formerly M5252)
4
1, 0, 36, 128, 386, 1024, 2488, 5632, 12031, 24576, 48308, 91904, 170110, 307200, 542872, 941056, 1602819, 2686976, 4439688, 7238272, 11657090, 18561024, 29242240, 45617664, 70507772 (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) ~ exp(sqrt(2*n)*Pi) / (2^(5/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
EXAMPLE
T8A = 1/q + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...
MATHEMATICA
nmax = 50; CoefficientList[Series[-8*x + Product[((1 - x^(2*k))*(1 - x^(4*k))/((1 - x^k)*(1 - x^(8*k))))^8, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 07 2017 *)
CROSSREFS
Cf. A045490.
Sequence in context: A250625 A057837 A352316 * A260130 A155708 A196891
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)