OFFSET
1,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
R. Mantaci and F. Rakotondrajao, Exceedingly deranging!, Advances in Appl. Math., 30 (2003), 177-188.
FORMULA
E.g.f.: (1/4)*z^2*(2-2*z+z^2)*exp(-z)/(1-z)^2.
a(n) = Sum_{k=1..n-1} k * A145880(n,k), n>=2.
a(n) ~ n!*exp(-1)*n/4. - Vaclav Kotesovec, Oct 07 2013
D-finite with recurrence +(-3*n+7)*a(n) +(3*n+2)*(n-3)*a(n-1) +(3*n^2-n+16)*a(n-2) +(3*n^2-23*n+32)*a(n-3) +(3*n-5)*(n-3)*a(n-4)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(4)=12 because the odd derangements of {1,2,3,4} are 4123, 3142, 4312, 2413, 2341 and 3421, having 1, 2, 2, 2, 3 and 2, excedances, respectively.
MAPLE
G:=(1/4)*z^2*(2-2*z+z^2)*exp(-z)/(1-z)^2: Gser:=series(G, z=0, 30): seq(factorial(n)*coeff(Gser, z, n), n=1..21);
MATHEMATICA
Rest[CoefficientList[Series[1/4*x^2*(2-2*x+x^2)*E^(-x)/(1-x)^2, {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 07 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 06 2008
STATUS
approved