A273160 a(n) = Sum_{k=1..n} C(n, floor((n-k)/k)).

0, 1, 3, 5, 10, 13, 30, 39, 84, 143, 290, 424, 1120, 1697, 3521, 6633, 14012, 22721, 53529, 88607, 189749, 356024, 730697, 1256272, 2889484, 5006918, 10399649, 19706342, 40954970, 72663140, 160499071, 286286349, 597385864, 1134282375, 2340807724, 4251969339

Offset: 0

Author

Wesley Ivan Hurt, May 16 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A051054, A273161.

Programs

Maple

A273160:=n->add(binomial(n,floor((n-i)/i)), i=1..n): seq(A273160(n), n=0..50);

Mathematica

Table[Sum[Binomial[n, Floor[(n - i)/i]], {i, n}], {n, 0, 40}]

Formula

a(n) ~ 2^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, May 28 2021