OFFSET
1,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
R. Mantaci and F. Rakotondrajao, Exceedingly deranging!, Advances in Appl. Math., 30 (2003), 177-188.
FORMULA
a(n) = Sum_{k=1..n-1} k*A145881(n,k), for n>=2.
E.g.f.: (1/4)*z^3*(2-z)*exp(-z)/(1-z)^2.
a(n) = 1/4*n*n!*Sum_{k=2..n-1} (-1)^k*(k+2)*(k-1)/(k+1)!. - Vaclav Kotesovec, Oct 28 2012
a(n) ~ n * n! / (4*exp(1)). - Vaclav Kotesovec, Dec 10 2021
D-finite with recurrence (-n+3)*a(n) +(n^2-3*n-2)*a(n-1) +(n-1)*(n+1)*a(n-2)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(4)=6 because the even derangements of {1,2,3,4} are 3412, 2143 and 4321, having 2, 2 and 2, excedances, respectively.
MAPLE
G:=(1/4)*z^3*(2-z)*exp(-z)/(1-z)^2: Gser:=series(G, z=0, 30): seq(factorial(n)*coeff(Gser, z, n), n=1..21);
MATHEMATICA
Table[1/4*n*n!*Sum[(-1)^k*(k+2)*(k-1)/(k+1)!, {k, 2, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 28 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 07 2008
STATUS
approved