%I #10 Feb 16 2019 04:25:31
%S 1,1,2,4,7,13,25,48,91,175,337,650,1258,2438,4735,9210,17940,34992,
%T 68331,133580,261391,511959,1003556,1968715,3864865,7592312,14923899,
%U 29352241,57761017,113723026,224010669,441452110,870326081,1716539232
%N a(1)=1, a(n)=ceiling(n/(n+1)*sum(k=1,n-1,a(k))).
%H Vaclav Kotesovec, <a href="/A082423/b082423.txt">Table of n, a(n) for n = 1..3300</a>
%F Apparently a(n) is asymptotic to C*2^n/sqrt(n) where C=0.6... [corrected by _Vaclav Kotesovec_, Feb 16 2019]
%F a(n) ~ c * 2^n / sqrt(n), where c = 0.6019481448829426024673784634152459777518844207090124563905577687332439... - _Vaclav Kotesovec_, Feb 16 2019
%t a[1]=1; a[n_]:=a[n]=Ceiling[n/(n+1)*Sum[a[k],{k,1,n-1}]]; Table[a[n], {n,1,40}] (* _Vaclav Kotesovec_, Feb 16 2019 *)
%K nonn
%O 1,3
%A _Benoit Cloitre_, Apr 24 2003