OFFSET
1,3
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.
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
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 *)
PROG
(PARI) vector(30, n, if(n, round(n!/exp(1)), 1)-(n+1)%2) \\ Altug Alkan, Nov 04 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Sedgewick reference from N. J. A. Sloane, Mar 07 2008
STATUS
approved