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McKay-Thompson series of class 8A for Monster.
(Formerly M5252)
4

%I M5252 #21 Oct 09 2017 19:10:17

%S 1,0,36,128,386,1024,2488,5632,12031,24576,48308,91904,170110,307200,

%T 542872,941056,1602819,2686976,4439688,7238272,11657090,18561024,

%U 29242240,45617664,70507772

%N McKay-Thompson series of class 8A for Monster.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A007265/b007265.txt">Table of n, a(n) for n = -1..1000</a>

%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F a(n) ~ exp(sqrt(2*n)*Pi) / (2^(5/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2017

%e T8A = 1/q + 36*q + 128*q^2 + 386*q^3 + 1024*q^4 + 2488*q^5 + 5632*q^6 + ...

%t 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 *)

%Y Cf. A045490.

%K nonn

%O -1,3

%A _N. J. A. Sloane_