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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

(list; graph; refs; listen; history; text; internal format)

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);

MATHEMATICA

A095718[n_]:= Sum[Floor[Binomial[n, k]/(k+1)], {k, 0, n}];

Table[A095718[n], {n, 40}] (* G. C. Greubel, Oct 20 2024 *)

PROG

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

(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

(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

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

URL: https://oeis.org/A095718

⇱ A095718 - OEIS