A051054 - OEIS

%I #24 Jan 06 2022 08:17:18

%S 0,1,3,7,15,26,54,85,159,292,513,804,1844,2965,5169,10679,20107,34120,

%T 72498,126028,245966,498852,913872,1644570,3600916,6530881,12280999,

%U 25149973,48355605,89310576,187976827,348475899,677303827

%N a(n) = Sum_{k=1..n} C(n, floor(n/k)).

%H Seiichi Manyama, <a href="/A051054/b051054.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) is asymptotic to 2^n/sqrt(n*Pi/2). - _Benoit Cloitre_, Jan 11 2003

%p A051054 := proc(n) local k; add(binomial(n,floor(n/k)), k=1..n); end; [seq(A051054(n), n=0..40)];

%t Table[Sum[Binomial[n, Floor[n/i]], {i, n}], {n, 0, 40}] (* _Wesley Ivan Hurt_, May 16 2016 *)

%o (PARI) a(n) = sum(k=1, n, binomial(n, n\k)); \\ _Seiichi Manyama_, Jan 06 2022

%Y Cf. A056045, A273160, A273161, A345466.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_