A051054 a(n) = Sum_{k=1..n} C(n, floor(n/k)).

0, 1, 3, 7, 15, 26, 54, 85, 159, 292, 513, 804, 1844, 2965, 5169, 10679, 20107, 34120, 72498, 126028, 245966, 498852, 913872, 1644570, 3600916, 6530881, 12280999, 25149973, 48355605, 89310576, 187976827, 348475899, 677303827

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A056045, A273160, A273161, A345466.

Programs

Maple

A051054 := proc(n) local k; add(binomial(n,floor(n/k)), k=1..n); end; [seq(A051054(n), n=0..40)];

Mathematica

Table[Sum[Binomial[n, Floor[n/i]], {i, n}], {n, 0, 40}] (* Wesley Ivan Hurt, May 16 2016 *)

PARI

a(n) = sum(k=1, n, binomial(n, n\k)); \\ Seiichi Manyama, Jan 06 2022

Formula

a(n) is asymptotic to 2^n/sqrt(n*Pi/2). - Benoit Cloitre, Jan 11 2003