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%I M4173 N1737 #28 Dec 04 2017 09:17:13
%S 1,6,27,98,309,882,2330,5784,13644,30826,67107,141444,289746,578646,
%T 1129527,2159774,4052721,7474806,13569463,24274716,42838245,74644794,
%U 128533884,218881098,368859591,615513678,1017596115,1667593666,2710062756,4369417452
%N Absolute value of coefficients of an elliptic function.
%D A. Cayley, A memoir on the transformation of elliptic functions, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 9, p. 128.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001940/b001940.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Cayley, <a href="/A001934/a001934.pdf">A memoir on the transformation of elliptic functions</a>, Philosophical Transactions of the Royal Society of London (1874): 397-456; Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, included in Vol. 9. [Annotated scan of pages 126-129]
%F G.f.: Product ( 1 - x^k )^(-c(k)), c(k) = 6, 6, 6, 0, 6, 6, 6, 0, ....
%F a(n) ~ 3^(1/4) * exp(sqrt(3*n)*Pi) / (128*sqrt(2)*n^(3/4)). - _Vaclav Kotesovec_, Nov 15 2017
%F G.f.: Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^6. - _Ilya Gutkovskiy_, Dec 04 2017
%t nn = 4*10; b = Flatten[Table[{6, 6, 6, 0}, {nn/4}]]; CoefficientList[x*Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x] (* _T. D. Noe_, Aug 17 2012 *)
%t nmax = 40; CoefficientList[Series[Product[((1 - x^(4*k)) / (1 - x^k))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 15 2017 *)
%Y Cf. A001935, A001936, A001937, A001939, A001941, A092877, A093160.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E Extended and corrected by _Simon Plouffe_
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