login
A051054
a(n) = Sum_{k=1..n} C(n, floor(n/k)).
5
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
0,3
LINKS
FORMULA
a(n) is asymptotic to 2^n/sqrt(n*Pi/2). - Benoit Cloitre, Jan 11 2003
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 *)
PROG
(PARI) a(n) = sum(k=1, n, binomial(n, n\k)); \\ Seiichi Manyama, Jan 06 2022
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved