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A004005
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Coefficients of elliptic function sn.
(Formerly M5397)
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3
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1, 135, 5478, 165826, 4494351, 116294673, 2949965020, 74197080276, 1859539731885, 46535238000235, 1163848723925346, 29100851707716150, 727566807977891803, 18189614152200873621, 454744658216502193656
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OFFSET
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2,2
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(5.2.24).
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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FORMULA
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a(n) = (5^(2*n+1) - (8*n-4)*3^(2*n+1) + 32*n^2 - 32*n -17)/256. - Vaclav Kotesovec after Fransen, Jul 30 2013
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MAPLE
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A004005:=-(-1-89*z+69*z**2+405*z**3)/(-1+25*z)/(9*z-1)**2/(z-1)**3; # Conjectured by Simon Plouffe in his 1992 dissertation.
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MATHEMATICA
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maxn = 16; se = Series[JacobiSN[u, m], {u, 0, 2*maxn+1}]; cc = Partition[CoefficientList[se, u], 2][[All, 2]]; cc2 = (CoefficientList[#, m] & /@ cc)*Table[(-1)^n*(2*n+1)!, {n, 0, maxn}]; Table[cc2[[n+1, n-1]], {n, 2, maxn}](* Jean-François Alcover, Feb 17 2012 *)
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CROSSREFS
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Leading terms in rows of triangle in A060628.
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
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STATUS
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approved
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