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A000270
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Number of discordant permutations.
(Formerly M3019 N1221)
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1
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1, 1, 0, 3, 16, 95, 672, 5397, 48704, 487917, 5373920, 64547175, 839703696, 11762247419, 176509466560, 2825125339305, 48040633506048, 864932233294681, 16436901752820288, 328791893988472843, 6905593482159150480, 151941269284478380119, 3495011687269591273312
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Touchard, Permutations discordant with two given permutations, Scripta Math., 19 (1953), 109-119.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..175
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FORMULA
| G.f.: G.f.: 1+(1-x)/(1+x)*Sum_{n>=0} n*n!*(x/(1+x)^2)^n. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 29 2007
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MAPLE
| a:= n-> coeftayl (1+ (1-x)/(1+x) *add (k*k! *(x/ (1+x)^2)^k, k=0..n), x=0, n): seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 24 2008]
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MATHEMATICA
| max = 20; f[x_] := 1+(1-x)/(1+x)*Sum[ n*n!*(x/(1+x)^2)^n, {n, 0, max}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* From Jean-François Alcover, Dec 09 2011, after Vladeta Jovovic *)
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CROSSREFS
| Sequence in context: A114174 A181067 A006347 * A157051 A000271 A157016
Adjacent sequences: A000267 A000268 A000269 * A000271 A000272 A000273
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 24 2008
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