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

1, 2, 5, 13, 27, 62, 125, 266, 538, 1106, 2213, 4509, 9019, 18166, 36365, 73012, 146025, 292658, 585317, 1171783, 2343697, 4689610, 9379221, 18763300, 37526628, 75062278, 150125100, 300268507, 600537015, 1201111598, 2402223197

Offset: 1

Author

Leroy Quet, Feb 09 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..3000 (terms 1..333 from Robert Israel)

Crossrefs

Cf. A014668, A320225.

Programs

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

Maple

A126656[1]:= 1:
for n from 2 to 100 do
  A126656[n]:= add(A126656[k]*floor(n/k),k=1..n-1);
od:
[seq(A126656[i],i=1..100)]; # Robert Israel, May 11 2014

Mathematica

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 *)

Formula

a(n) is asymptotic to c*2^n where c=1.1186567921399193608303756752855835542518061417771006467002421299046146... [Benoit Cloitre, Nov 10 2009]

Extensions

Extended by Ray Chandler, Feb 11 2007