A242569 a(n) = n! - 2*n.

1, -1, -2, 0, 16, 110, 708, 5026, 40304, 362862, 3628780, 39916778, 479001576, 6227020774, 87178291172, 1307674367970, 20922789887968, 355687428095966, 6402373705727964, 121645100408831962, 2432902008176639960, 51090942171709439958, 1124000727777607679956, 25852016738884976639954, 620448401733239439359952

Offset

0,3

Comments

For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is an integer.

For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is prime.

For n > 1, a(n) is even.

Links

Table of n, a(n) for n=0..24.

Formula

E.g.f.: 1/(1 - x) - 2*x*exp(x). - Stefano Spezia, Sep 24 2025

Example

3! - 2*3 = 0 so a(3) = 0.
4! - 2*4 = 16 so a(4) = 16.
5! - 2*5 = 110 so a(5) = 110.

Mathematica

Table[n!-2n, {n, 0, 30}] (* Harvey P. Dale, Oct 22 2024 *)

Prog

(Python)
import math
{print(math.factorial(n)-2*n) for n in range(0, 25)}
(PARI) for(n=0, 25, print(n!-2*n))

Crossrefs

Cf. A000142, A242567, A242568.

Sequence in context: A345652 A009528 A178987 * A152154 A324665 A349036

Adjacent sequences: A242566 A242567 A242568 * A242570 A242571 A242572

Keyword

sign

Author

Derek Orr, May 17 2014

Extensions

a(0) = 1 prepended by Stefano Spezia, Sep 24 2025

Status

approved