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 A072948 Number of permutations p of (1,2,3,...,2n) such that sum(k=1,2n,abs(k-p(k)))=2n. 1
 1, 7, 46, 327, 2350, 17222, 127508, 952299, 7159090, 54107670, 410729140, 3129241874, 23914923644, 183254996828, 1407497158968, 10832287881639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Mathieu Guay-Paquey and T. Kyle Petersen, The generating function for total displacement, arXiv:1404.4674 [math.CO], 2014. FORMULA This is impossible if the number of symbols is odd. MATHEMATICA f[n_] := If[n == 1, 1, Floor[n/2] t^Floor[(n - 1)/2] z]; F[t_, z_] = ContinuedFractionK[f[i], 1, {i, 1, 8}]; a[n_] := a[n] = SeriesCoefficient[F[t, z], {z, 0, 2 n}, {t, 0, n}]; Table[Print[n, " ", a[n]]; a[n], {n, 1, 15}] (* Jean-François Alcover, Feb 25 2019 *) PROG (PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, abs(i-component(numtoperm(n, k), i)))-n, 0, 1)) CROSSREFS Cf. A072949, A062869. Sequence in context: A244265 A240722 A067318 * A332852 A178962 A203267 Adjacent sequences:  A072945 A072946 A072947 * A072949 A072950 A072951 KEYWORD more,nonn AUTHOR Benoit Cloitre, Aug 20 2002 EXTENSIONS a(5) from Michel ten Voorde Jun 13 2003 a(6) from Ryan Propper, Mar 26 2007 a(7)-a(8) from Sean A. Irvine, Sep 22 2009 a(9)-a(12) from Robert Gerbicz, Nov 27 2010 a(13)-a(16) from Alois P. Heinz, May 02 2014 using formula given by Guay-Paquey and Petersen STATUS approved

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Last modified September 19 22:06 EDT 2021. Contains 347576 sequences. (Running on oeis4.)