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A145881 Triangle read by rows: T(n,k) is the number of even permutations of {1,2,...,n} with no fixed points and having k excedances (n>=1; k>=1).

%I A145881 #17 Jul 22 2017 08:33:43
%S A145881 0,0,1,1,0,3,0,1,11,11,1,0,25,80,25,0,1,57,407,407,57,1,0,119,1680,
%T A145881 3815,1680,119,0,1,247,6211,26917,26917,6211,247,1,0,501,21432,160053,
%U A145881 303504,160053,21432,501,0,1,1013,70775,852347,2747009,2747009,852347,70775
%N A145881 Triangle read by rows: T(n,k) is the number of even permutations of {1,2,...,n} with no fixed points and having k excedances (n>=1; k>=1).
%C A145881 Row n has n-1 entries (n>=2).
%C A145881 Sum of entries in row n = A000321(n).
%C A145881 Sum_{k=1..n-1} k*T(n,k) = A145887(n) (n>=2).
%H A145881 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 A145881 E.g.f.: ((1-t)*exp(-tz)/(1-t*exp((1-t)z)) - (t*exp(-z)-exp(-tz))/(1-t))/2.
%e A145881 T(4,2)=3 because the even derangements of {1,2,3,4} are 3412, 2143 and 4321.
%e A145881 Triangle starts:
%e A145881   0;
%e A145881   0;
%e A145881   1,  1;
%e A145881   0,  3,  0;
%e A145881   1, 11, 11,  1;
%e A145881   0, 25, 80, 25,  0;
%p A145881 G:=((1-t)*exp(-t*z)/(1-t*exp((1-t)*z))-(t*exp(-z)-exp(-t*z))/(1-t))*1/2: Gser:=simplify(series(G,z=0,15)): for n to 11 do P[n]:=sort(expand(factorial(n)*coeff(Gser,z,n))) end do: 0; for n to 11 do seq(coeff(P[n],t,j),j=1..n-1) end do; # yields sequence in triangular form
%Y A145881 Cf. A000321, A145880, A145886, A145887.
%K A145881 nonn,tabf
%O A145881 1,6
%A A145881 _Emeric Deutsch_, Nov 06 2008
%E A145881 Formula corrected by _Jon E. Schoenfield_, Jul 21 2017 at the request of the author