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A145886 Number of excedances in all odd permutations of {1,2,...,n} with no fixed points. 5
0, 1, 0, 12, 50, 405, 3234, 29680, 300348, 3337425, 40382540, 528644556, 7445076990, 112248853717, 1803999433950, 30788257007040, 556112892188504, 10598857474652865, 212565974908314168, 4475073155964510700 (list; graph; refs; listen; history; text; internal format)
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

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

Cf. A145880, A145881, A145887.

Sequence in context: A248230 A083559 A051797 * A268351 A166776 A200887

Adjacent sequences:  A145883 A145884 A145885 * A145887 A145888 A145889

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 06 2008

STATUS

approved

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Last modified October 15 15:33 EDT 2018. Contains 316236 sequences. (Running on oeis4.)