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 A095718 #16 Oct 21 2024 04:32:31
%S A095718 1,2,3,6,9,18,30,56,101,186,339,630,1167,2182,4092,7710,14561,27594,
%T A095718 52425,99862,190647,364722,699045,1342176,2581107,4971024,9586975,
%U A095718 18512790,35791386,69273666,134217720,260301046,505290269,981706808
%N A095718 a(n) = Sum_{k=0..n} floor(binomial(n,k)/(k+1)).
%C A095718 Row sums of A011847.
%H A095718 Robert Israel, <a href="/A095718/b095718.txt">Table of n, a(n) for n = 1..3329</a>
%F A095718 a(n) = Sum_{k=0..n} floor(binomial(n,k)/(k+1)).
%F A095718 From _Robert Israel_, May 07 2018: (Start)
%F A095718 (2^(n+1)-1)/(n+1) >= a(n) >= (2^(n+1)-1)/(n+1) - n.
%F A095718 It appears that a(n) = (2^(n+1)-2)/(n+1) if n+1 is prime. (End)
%p A095718 a:=n->add(floor(combinat[numbcomb](n,k)/(k+1)),k=0..n);
%t A095718 A095718[n_]:= Sum[Floor[Binomial[n,k]/(k+1)], {k,0,n}];
%t A095718 Table[A095718[n], {n,40}] (* _G. C. Greubel_, Oct 20 2024 *)
%o A095718 (PARI) a(n) = sum(k=0, n, binomial(n,k)\(k+1)); \\ _Michel Marcus_, May 08 2018
%o A095718 (Magma)
%o A095718 A095718:= func< n | (&+[Floor(Binomial(n,k)/(k+1)): k in [0..n]]) >;
%o A095718 [A095718(n): n in [1..40]]; // _G. C. Greubel_, Oct 20 2024
%o A095718 (SageMath)
%o A095718 def A095718(n): return sum(binomial(n,k)//(k+1) for k in range(n+1))
%o A095718 [A095718(n) for n in range(1,41)] # _G. C. Greubel_, Oct 20 2024
%Y A095718 Cf. A011847, A101687.
%K A095718 nonn
%O A095718 1,2
%A A095718 _Mike Zabrocki_, Jul 08 2004