A012264 Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• James Propp, posting to math-fun mailing list May 30 1997.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A012265.

Programs

Maple

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:

Mathematica

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 *)

Extensions

More terms from James Sellers