

A329851


Sum of absolute values of nth differences over all permutations of {0, 1, ..., n}.


0



0, 2, 12, 120, 1320, 17856, 273056, 4772624, 92626944, 1986317024, 46556867456, 1184827221584, 32524270418432, 958020105786536
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OFFSET

0,2


COMMENTS

a(n) <= ((n+1)!  2*A131502(n))*A130783(n).
Every term is even because the nth difference of a permutation and its reversal are the same up to sign.


LINKS

Table of n, a(n) for n=0..13.


EXAMPLE

For n = 2, the second differences of the (2+1)! = 6 permutations of {0,1,2} are:
[0,1,2] > [1, 1] > 0,
[0,2,1] > [2,1] > 3,
[1,0,2] > [1, 2] > 3,
[1,2,0] > [1,2] > 3,
[2,0,1] > [2, 1] > 3, and
[2,1,0] > [1,1] > 0.
The sum of the absolute values of these second differences is 0 + 3 + 3 + 3 + 3 + 0 = 12.


MATHEMATICA

a[n_] := Block[{x, k}, k = CoefficientList[(x  1)^n, x]; Sum[Abs[k.p], {p, Permutations@ Range[0, n]}]]; Array[a, 10, 0] (* Giovanni Resta, Nov 23 2019 *)


CROSSREFS

Cf. A130783, A131502, A327845.
Sequence in context: A089431 A119701 A286629 * A127112 A003580 A052580
Adjacent sequences: A329848 A329849 A329850 * A329852 A329853 A329854


KEYWORD

nonn,more


AUTHOR

Peter Kagey, Nov 22 2019


EXTENSIONS

a(10) from Alois P. Heinz, Nov 22 2019
a(11)a(13) from Giovanni Resta, Nov 23 2019


STATUS

approved



