A366978 a(n) = Sum_{j=1..n} binomial(floor(n/j)+n,n+1).

1, 5, 17, 64, 220, 839, 3061, 11684, 44126, 169432, 648589, 2505411, 9670165, 37497431, 145502481, 566076182, 2204451031, 8599761208, 33581164151, 131296796355, 513812162117, 2012709456997, 7890502860027, 30958303856804, 121549519502347, 477555096290870, 1877411492125154

Offset: 1

Author

Chai Wah Wu, Oct 30 2023

Keywords

• nonn

Crossrefs

Superdiagonal of array in A366977.

Programs

Mathematica

Table[Sum[Binomial[j+n-1,n]Floor[n/j],{j,n}],{n,30}] (* Harvey P. Dale, Jul 19 2024 *)

Python

from math import isqrt, comb
def A366978(n): return (-(s:=isqrt(n))**2*comb(s+n,n)+sum((q:=n//j)*((n+1)*comb(j+n-1,n)+comb(q+n,n)) for j in range(1,s+1)))//(n+1)

Formula

a(n) = Sum_{j=1..n} binomial(j+n-1,n)*floor(n/j).

a(n) ~ 4^n / sqrt(Pi*n). - Vaclav Kotesovec, Sep 19 2024