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 A245269 #17 May 25 2025 01:40:37
%S A245269 1,3,7,15,31,63,127,254,502,978,1882,3600,6904,13380,26332,52664,
%T A245269 106744,218232,447736,917760,1873312,3799920,7653136,15306272,
%U A245269 30429856,60234528,118956831,234885092,464595690,921868388,1836393687,3672648928,7369572624,14821243232
%N A245269 Sum of binomial(n,k) over cubefree k.
%H A245269 Eric M. Schmidt, <a href="/A245269/b245269.txt">Table of n, a(n) for n = 1..1000</a>
%H A245269 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 A245269 a(n) ~ 2^n/zeta(3). [Take p = 1/2 in Nymann and Leahey.]
%t A245269 cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; a[n_] := Sum[Binomial[n, k], {k, Select[Range[n], cubeFreeQ]}]; Array[a, 34] (* _Amiram Eldar_, May 25 2025 *)
%o A245269 (Sage) def A245269(n) : return sum(binomial(n,k) for k in range(1,n+1) if all(m <= 2 for (p,m) in factor(k)))
%Y A245269 Cf. A013928, A060431, A245268.
%K A245269 nonn
%O A245269 1,2
%A A245269 _Eric M. Schmidt_, Jul 15 2014