A095718 a(n) = Sum_{k=0..n} floor(binomial(n,k)/(k+1)).

1, 2, 3, 6, 9, 18, 30, 56, 101, 186, 339, 630, 1167, 2182, 4092, 7710, 14561, 27594, 52425, 99862, 190647, 364722, 699045, 1342176, 2581107, 4971024, 9586975, 18512790, 35791386, 69273666, 134217720, 260301046, 505290269, 981706808

Offset: 1

Author

Mike Zabrocki, Jul 08 2004

Keywords

• nonn

Comments

Row sums of A011847.

Links

• Robert Israel, Table of n, a(n) for n = 1..3329

Crossrefs

Cf. A011847, A101687.

Programs

Magma

A095718:= func< n | (&+[Floor(Binomial(n,k)/(k+1)): k in [0..n]]) >;
[A095718(n): n in [1..40]]; // G. C. Greubel, Oct 20 2024

Maple

a:=n->add(floor(combinat[numbcomb](n,k)/(k+1)),k=0..n);

Mathematica

A095718[n_]:= Sum[Floor[Binomial[n,k]/(k+1)], {k,0,n}];
Table[A095718[n], {n,40}] (* G. C. Greubel, Oct 20 2024 *)

PARI

a(n) = sum(k=0, n, binomial(n,k)\(k+1)); \\ Michel Marcus, May 08 2018

SageMath

def A095718(n): return sum(binomial(n,k)//(k+1) for k in range(n+1))
[A095718(n) for n in range(1,41)] # G. C. Greubel, Oct 20 2024

Formula

a(n) = Sum_{k=0..n} floor(binomial(n,k)/(k+1)).

From Robert Israel, May 07 2018: (Start)

(2^(n+1)-1)/(n+1) >= a(n) >= (2^(n+1)-1)/(n+1) - n.

It appears that a(n) = (2^(n+1)-2)/(n+1) if n+1 is prime. (End)