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A012264
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Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.
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2
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1, 3, 1, 3, 5, 3, 5, 7, 5, 7, 5, 7, 9, 7, 9, 7, 9, 11, 9, 11, 13, 11, 13, 11, 13, 15, 13, 15, 17, 15, 17, 15, 17, 19, 17, 19, 17, 19, 21, 19, 21, 23, 21, 23, 21, 23, 25, 23, 25, 23, 25, 27, 25, 27, 29, 27, 29, 27, 29, 31, 29, 31, 33
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OFFSET
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0,2
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REFERENCES
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James Propp, posting to math-fun mailing list May 30 1997.
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LINKS
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MAPLE
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Digits := 25: t1 := 0: for k from 1 by 2 to 51 do t1 := t1+(-1)^( (k-1)/2 )*x^k/k!; print(nops([ fsolve(t1*k!) ])); od:
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MATHEMATICA
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f[n_] := Sum[ (-1)^k*x^(2k+1)/(2k+1)!, {k, 0, n}]; a[n_] := CountRoots[f[n], x]; Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Sep 13 2012 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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