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Search: id:A145881
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| A145881 |
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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). |
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+0
4
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| 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, 3815, 1680, 119, 0, 1, 247, 6211, 26917, 26917, 6211, 247, 1, 0, 501, 21432, 160053, 303504, 160053, 21432, 501, 0, 1, 1013, 70775, 852347, 2747009, 2747009, 852347, 70775
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Row n has n-1 entries (n>=2).
Sum of entries in row n = A000321(n).
Sum(k*T(n,k),k=1..n-1)=A145887(n) (n>=2).
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REFERENCES
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R. Mantaci and F. Rakotondrajao, Exceedingly deranging!, Advances in Appl. Math., 30 (2003), 177-188.
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FORMULA
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E.g.f.=Sum(t^exc(p)*z^n/n!)=[(1-t)*exp(-tz)/(1-t*exp((1-t)z))-(t*exp(-z)-exp(-tz))/(1-t)]/2.
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EXAMPLE
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T(4,2)=3 because the even derangements of {1,2,3,4} are 3412, 2143 and 4321.
Triangle starts:
0;
0;
1,1;
0,3,0;
1,11,11,1;
0,25,80,25,0;
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MAPLE
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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
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CROSSREFS
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A000321, A145887, A145880, A145886
Sequence in context: A058175 A112906 A137375 this_sequence A135313 A022695 A067169
Adjacent sequences: A145878 A145879 A145880 this_sequence A145882 A145883 A145884
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 06 2008
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