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

1,2

Comments

Row sums of A011847.

Links

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

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)

Maple

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

Prog

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

Crossrefs

Cf. A011847, A101687.

Sequence in context: A018499 A107847 A059966 * A038751 A218543 A266925

Adjacent sequences: A095715 A095716 A095717 * A095719 A095720 A095721

Keyword

nonn

Author

Mike Zabrocki, Jul 08 2004

Status

approved