A262376 a(n) = Sum_{k=0..n} (k! - k).

1, 1, 1, 4, 24, 139, 853, 5886, 46198, 409069, 4037859, 43954648, 522956236, 6749977023, 93928268209, 1401602636194, 22324392524178, 378011820620161, 6780385526348143, 128425485935180124, 2561327494111820104, 53652269665821260083, 1177652997443428940061

Offset: 0

Author

Daniel Suteu, Sep 20 2015

Keywords

• nonn
• easy

Examples

			a(3) = 4, which is the following sum: (0!-0) + (1!-1) + (2!-2) + (3!-3).
		

Links

• Daniel Suteu, Table of n, a(n) for n = 0..100

Crossrefs

Partial sums of A005096.

Cf. A003422, A000217.

Programs

Mathematica

Table[Sum[k! - k, {k, 0, n}], {n, 0, 22}] (* Michael De Vlieger, Sep 21 2015 *)

PARI

a(n)=sum(i=0,n,i!-i) \\ Anders Hellström, Sep 20 2015

Sidef

var sum = 0;
range(0, 10).each { |n|
    sum += (n! - n);
    say(n, "\t", sum);
};

Formula

a(n) = Sum_{k=0..n} k! - k.

a(n) = A003422(n+1) - A000217(n). - Altug Alkan, Sep 20 2015