%I #27 May 28 2021 03:49:52

%S 1,5,13,33,61,143,246,521,985,1995,3499,7923,14028,28642,55603,115369,

%T 210665,455399,838338,1755983,3383652,6974159,13034492,28011611,

%U 52475486,108821068,210050941,436273458,824191369,1744975533,3301974301,6867107913,13250454241

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

%H Robert Israel, <a href="/A308812/b308812.txt">Table of n, a(n) for n = 1..3318</a>

%F a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} binomial(n,k) * x^k/(1 - x^k).

%F a(n) = Sum_{k=1..n} Sum_{d|k} binomial(n,d).

%F a(n) ~ 3 * 2^(n-1). - _Vaclav Kotesovec_, May 28 2021

%p f:= proc(n) local k; add(binomial(n,k)*floor(n/k),k=1..n) end proc:

%p map(f, [$1..100]); # _Robert Israel_, Aug 23 2019

%t Table[Sum[Binomial[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 33}]

%t Table[SeriesCoefficient[1/(1 - x) Sum[Binomial[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 33}]

%t Table[Sum[Sum[Binomial[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 33}]

%Y Cf. A056045.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 22 2019