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A049061
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Triangle a(n,k) (1<=k<=n) of "signed Eulerian numbers" read by rows.
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4
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1, 1, -1, 1, 0, -1, 1, -1, -1, 1, 1, 2, -6, 2, 1, 1, 1, -8, 8, -1, -1, 1, 8, -19, 0, 19, -8, -1, 1, 7, -27, 19, 19, -27, 7, 1, 1, 22, -32, -86, 190, -86, -32, 22, 1, 1, 21, -54, -54, 276, -276, 54, 54, -21, -1, 1, 52, 27, -648, 1002, 0, -1002, 648, -27, -52, -1, 1, 51, -25
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Identical to rows n=2..n of D(n,k) on page 2 of Tanimoto reference. - Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 11 2006
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REFERENCES
| Desarmenien, Jacques; Foata, Dominique; The signed Eulerian numbers. Discrete Math. 99 (1992), number 1-3, 49-58.
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LINKS
| J. Desarmenien and D. Foata, The signed Eulerian Numbers
Shinji Tanimoto, Parity-Alternate Permutations and Signed Eulerian Numbers, math.CO/0612135.
S. Tanimoto, A new approach to signed Eulerian numbers
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FORMULA
| a(2n, k)=a(2n-1, k)-a(2n-1, k-1), a(2n+1, k) = k*a(2n, k)+(2n-k+2)*a(2n, k-1).
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EXAMPLE
| 1; 1,-1; 1,0,-1; 1,-1,-1,1; 1,2,-6,2,1; ...
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MATHEMATICA
| a[n_ /; EvenQ[n] && n > 0, k_] := a[n, k] = a[n - 1, k] - a[n - 1, k - 1]; a[n_ /; OddQ[n] && n > 0, k_] := a[n, k] = k*a[n - 1, k] + (n - k + 1)*a[n - 1, k - 1]; a[0, _]=0; a[1, 1]=1; Flatten[Table[a[n, k], {n, 12}, {k, n}]] (* From Jean-François Alcover, May 02 2011 *)
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CROSSREFS
| Cd. A008292.
Sequence in context: A168294 A004544 A010590 * A082516 A204935 A008905
Adjacent sequences: A049058 A049059 A049060 * A049062 A049063 A049064
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KEYWORD
| sign,easy,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Apr 12 2000
ArXiv URL replaced by its non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 23 2009
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