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%I #8 Feb 26 2020 14:46:48
%S 1,1,2,5,13,35,92,246,646,1705,4475,11755,30790,80738,211424,553780,
%T 1449999,3796903,9940710,26027151,68140743,178399767,467059142,
%U 1222789414,3201309100,8381170779,21942203523,57445520528,150394362117,393737778753,1030818974142
%N a(1)=1; a(n+1) = Sum_{k=1 to n} a(k) a(ceiling(n/k)).
%H G. C. Greubel, <a href="/A097919/b097919.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) ~ c * ((3 + sqrt(5))/2)^n, where c = 0.113749340218250534902880196020226926353440247305682768150354123166912... - _Vaclav Kotesovec_, Feb 26 2020
%p f:=proc(n) option remember; local k; if n = 1 then RETURN(1); fi; add( f(k)*f(ceil((n-1)/k)), k=1..n-1 ); end;
%t a[1] := 1; a[n_] := a[n] = Sum[a[k]*a[Ceiling[(n - 1)/k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 30}] (* _G. C. Greubel_, Dec 20 2017 *)
%Y Cf. A097417.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, following a suggestion of Benoit Cloitre, Sep 03 2004
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