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A145887 Number of excedances in all even permutations of {1,2,...,n} with no fixed points.

%I A145887 #21 Jul 26 2022 15:44:47
%S A145887 0,0,3,6,60,390,3255,29652,300384,3337380,40382595,528644490,
%T A145887 7445077068,112248853626,1803999434055,30788257006920,556112892188640,
%U A145887 10598857474652712,212565974908314339,4475073155964510510
%N A145887 Number of excedances in all even permutations of {1,2,...,n} with no fixed points.
%H A145887 Vincenzo Librandi, <a href="/A145887/b145887.txt">Table of n, a(n) for n = 1..200</a>
%H A145887 R. Mantaci and F. Rakotondrajao, <a href="http://dx.doi.org/10.1016/S0196-8858(02)00531-6">Exceedingly deranging!</a>, Advances in Appl. Math., 30 (2003), 177-188.
%F A145887 a(n) = Sum_{k=1..n-1} k*A145881(n,k), for n>=2.
%F A145887 E.g.f.: (1/4)*z^3*(2-z)*exp(-z)/(1-z)^2.
%F A145887 a(n) = 1/4*n*n!*Sum_{k=2..n-1} (-1)^k*(k+2)*(k-1)/(k+1)!. - _Vaclav Kotesovec_, Oct 28 2012
%F A145887 a(n) ~ n * n! / (4*exp(1)). - _Vaclav Kotesovec_, Dec 10 2021
%F A145887 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
%e A145887 a(4)=6 because the even derangements of {1,2,3,4} are 3412, 2143 and 4321, having 2, 2 and 2, excedances, respectively.
%p A145887 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);
%t A145887 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 *)
%Y A145887 Cf. A145880, A145881, A145886.
%K A145887 nonn
%O A145887 1,3
%A A145887 _Emeric Deutsch_, Nov 07 2008