A014508 a(n) = floor( n! / e ).

0, 0, 2, 8, 44, 264, 1854, 14832, 133496, 1334960, 14684570, 176214840, 2290792932, 32071101048, 481066515734, 7697064251744, 130850092279664, 2355301661033952, 44750731559645106, 895014631192902120

Offset: 1

Author

Simon Plouffe

Keywords

• nonn
• easy

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100
• Michael Penn, Always even., YouTube video, 2022.
• R. Sedgewick, Permutation generation methods, Computing Surveys, 9 (1977), 137-164.

Crossrefs

Cf. A000166.

Programs

Mathematica

f[n_] := Floor[n!/E]; Array[f, 20] (* or *) a[0] = 1; a[n_] := a[n] = n*a[n - 1] + (-1)^n; f[n_] := Sum[(n - k - 1) a[n - k - 1], {k, 0, n - 1}]; Array[f, 20] (* Robert G. Wilson v, Apr 01 2011 *)

PARI

vector(30, n, if(n,round(n!/exp(1)), 1)-(n+1)%2) \\ Altug Alkan, Nov 04 2015

Formula

a(n) = Sum_{k=0..n-1} (n - k - 1)*A000166(n - k - 1). - Robert G. Wilson v, Apr 01 2011

a(n) = A000166(n) - (n mod 2). - Joerg Arndt, Apr 02 2011

E.g.f.: -exp(x)/2-(x+1)*exp(-x)/(2*x-2). - Mark van Hoeij, Oct 30 2011

Extensions

Sedgewick reference from N. J. A. Sloane, Mar 07 2008