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Search: id:A145880
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| A145880 |
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Triangle read by rows: T(n,k) is the number of odd permutations of {1,2,...,n} with no fixed points and having k excedances (n>=1; k>=1). |
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4
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| 0, 1, 0, 0, 1, 4, 1, 0, 10, 10, 0, 1, 26, 81, 26, 1, 0, 56, 406, 406, 56, 0, 1, 120, 1681, 3816, 1681, 120, 1, 0, 246, 6210, 26916, 26916, 6210, 246, 0, 1, 502, 21433, 160054, 303505, 160054, 21433, 502, 1, 0, 1012, 70774, 852346, 2747008, 2747008, 852346, 70774
(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 = A000387(n)=A145221(n).
Sum(k*T(n,k),k=1..n-1)=A145886(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)=4 because the odd derangements of {1,2,3,4} with 2 excedances are 3142, 4312, 2413 and 3421.
Triangle starts:
0;
1;
0,0;
1,4,1;
0,10,10,0;
1,26,81,26,1;
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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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A000387, A145221, A145886, A145881, A145887
Sequence in context: A095831 A089962 A127155 this_sequence A048516 A060638 A007789
Adjacent sequences: A145877 A145878 A145879 this_sequence A145881 A145882 A145883
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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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