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A001940
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Absolute value of coefficients of an elliptic function.
(Formerly M4173 N1737)
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6
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1, 6, 27, 98, 309, 882, 2330, 5784, 13644, 30826, 67107, 141444, 289746, 578646, 1129527, 2159774, 4052721, 7474806, 13569463, 24274716, 42838245, 74644794, 128533884, 218881098, 368859591, 615513678, 1017596115, 1667593666, 2710062756, 4369417452
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OFFSET
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0,2
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REFERENCES
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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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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A. Cayley, A memoir on the transformation of elliptic functions, 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]
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FORMULA
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G.f.: Product ( 1 - x^k )^(-c(k)), c(k) = 6, 6, 6, 0, 6, 6, 6, 0, ....
a(n) ~ 3^(1/4) * exp(sqrt(3*n)*Pi) / (128*sqrt(2)*n^(3/4)). - Vaclav Kotesovec, Nov 15 2017
G.f.: Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^6. - Ilya Gutkovskiy, Dec 04 2017
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MATHEMATICA
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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 *)
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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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