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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

Table of n, a(n) for n=1..16.

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-Fran├žois 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.)