|
%I #15 Dec 16 2021 22:38:42
%S 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,
%T 15,17,15,17,19,17,19,17,19,21,19,21,23,21,23,21,23,25,23,25,23,25,27,
%U 25,27,29,27,29,27,29,31,29,31,33
%N Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.
%D _James Propp_, posting to math-fun mailing list May 30 1997.
%H Vincenzo Librandi, <a href="/A012264/b012264.txt">Table of n, a(n) for n = 0..200</a>
%p 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:
%t 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 *)
%Y Cf. A012265.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_
|
