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 A245268 #28 May 25 2025 01:40:33
%S A245268 1,3,7,14,26,48,92,184,375,758,1497,2884,5461,10286,19507,37584,73866,
%T A245268 147987,301075,618794,1278116,2640993,5439593,11138764,22640100,
%U A245268 45644797,91293390,181301470,358024924,704359427,1383415456,2718141072,5351701032,10570658330
%N A245268 Sum of binomial(n,k) over squarefree k.
%H A245268 Eric M. Schmidt, <a href="/A245268/b245268.txt">Table of n, a(n) for n = 1..1000</a>
%H A245268 J. E. Nymann and W. J. Leahey, <a href="http://dx.doi.org/10.1216/RMJ-1977-7-4-769">On the probability that an integer chosen according to the binomial distribution be k-free</a>, Rocky Mountain Journal of Mathematics 7 (1977), no. 4, 769-774.
%F A245268 a(n) ~ 2^n/zeta(2). [Take p = 1/2 in Nymann and Leahey.]
%t A245268 a[n_] := Sum[Binomial[n, k], {k, Select[Range[n], SquareFreeQ]}]; Array[a, 34] (* _Amiram Eldar_, May 25 2025 *)
%o A245268 (Sage) def A235268(n) : return sum(binomial(n,k) for k in range(1,n+1) if is_squarefree(k))
%o A245268 (PARI) a(n) = sum(k=1, n, if (issquarefree(k), binomial(n,k), 0)); \\ _Michel Marcus_, Jul 16 2014
%Y A245268 Cf. A013928, A060431, A245269.
%K A245268 nonn
%O A245268 1,2
%A A245268 _Eric M. Schmidt_, Jul 15 2014