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A126656 a(1)=1; for n>1, a(n) = Sum_{k=1..n-1} a(k) * floor(n/k).

%I A126656 #35 Sep 08 2022 08:45:29
%S A126656 1,2,5,13,27,62,125,266,538,1106,2213,4509,9019,18166,36365,73012,
%T A126656 146025,292658,585317,1171783,2343697,4689610,9379221,18763300,
%U A126656 37526628,75062278,150125100,300268507,600537015,1201111598,2402223197
%N A126656 a(1)=1; for n>1, a(n) = Sum_{k=1..n-1} a(k) * floor(n/k).
%H A126656 Seiichi Manyama, <a href="/A126656/b126656.txt">Table of n, a(n) for n = 1..3000</a> (terms 1..333 from Robert Israel)
%F A126656 a(n) is asymptotic to c*2^n where c=1.1186567921399193608303756752855835542518061417771006467002421299046146... [_Benoit Cloitre_, Nov 10 2009]
%p A126656 A126656[1]:= 1:
%p A126656 for n from 2 to 100 do
%p A126656   A126656[n]:= add(A126656[k]*floor(n/k),k=1..n-1);
%p A126656 od:
%p A126656 [seq(A126656[i],i=1..100)]; # _Robert Israel_, May 11 2014
%t A126656 f[l_List] := Block[{n = Length[l] + 1},Append[l, Sum[l[[k]]*Floor[n/k], {k, n - 1}]]];Nest[f, {1}, 32] (* _Ray Chandler_, Feb 11 2007 *)
%o A126656 (Magma) sol:=[1]; for n in [2..31] do Append(~sol, &+[sol[k]*Floor(n/k):k in [1..n-1]]); end for; sol; // _Marius A. Burtea_, Sep 07 2019
%Y A126656 Cf. A014668, A320225.
%K A126656 nonn
%O A126656 1,2
%A A126656 _Leroy Quet_, Feb 09 2007
%E A126656 Extended by _Ray Chandler_, Feb 11 2007