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a(n) ~ 3 * 2^(n-1). - Vaclav Kotesovec, May 28 2021
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Robert Israel, <a href="/A308812/b308812.txt">Table of n, a(n) for n = 1..3318</a>
f:= proc(n) local k; add(binomial(n, k)*floor(n/k), k=1..n) end proc:
map(f, [$1..100]); # Robert Israel, Aug 23 2019
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a(n) = Sum_{k=1..n} binomial(n,k) * floor(n/k).
1, 5, 13, 33, 61, 143, 246, 521, 985, 1995, 3499, 7923, 14028, 28642, 55603, 115369, 210665, 455399, 838338, 1755983, 3383652, 6974159, 13034492, 28011611, 52475486, 108821068, 210050941, 436273458, 824191369, 1744975533, 3301974301, 6867107913, 13250454241
1,2
a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} binomial(n,k) * x^k/(1 - x^k).
a(n) = Sum_{k=1..n} Sum_{d|k} binomial(n,d).
Table[Sum[Binomial[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 33}]
Table[SeriesCoefficient[1/(1 - x) Sum[Binomial[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 33}]
Table[Sum[Sum[Binomial[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 33}]
Cf. A056045.
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Ilya Gutkovskiy, Aug 22 2019
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