This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A012264 #16 Jul 02 2025 16:01:55
%S A012264 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 A012264 15,17,15,17,19,17,19,17,19,21,19,21,23,21,23,21,23,25,23,25,23,25,27,
%U A012264 25,27,29,27,29,27,29,31,29,31,33
%N A012264 Number of real roots of x - x^3/3! + x^5/5! - ... + (-1)^n*x^(2n+1)/(2n+1)!.
%D A012264 _James Propp_, posting to math-fun mailing list May 30 1997.
%H A012264 Vincenzo Librandi, <a href="/A012264/b012264.txt">Table of n, a(n) for n = 0..200</a>
%p A012264 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 A012264 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 A012264 Cf. A012265.
%K A012264 nonn,nice
%O A012264 0,2
%A A012264 _N. J. A. Sloane_
%E A012264 More terms from _James Sellers_