A273161 a(n) = Sum_{k=1..n} C(n-k, floor((n-k)/k)).

0, 1, 2, 3, 5, 7, 13, 19, 34, 61, 108, 174, 384, 641, 1166, 2337, 4458, 7828, 16421, 29346, 57231, 114126, 215915, 396491, 839324, 1549146, 2983185, 5978656, 11628952, 21812113, 45099914, 84842925, 166417181, 332267593, 647614074, 1234586894, 2538571022

Offset: 0

Author

Wesley Ivan Hurt, May 16 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A051054, A273160.

Programs

Maple

A273161:=n->add(binomial(n-i,floor((n-i)/i)), i=1..n): seq(A273161(n), n=0..50);

Mathematica

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

Formula

a(n) ~ 2^(n - 3/2) / sqrt(Pi*n). - Vaclav Kotesovec, May 28 2021