A018927 For each permutation p of {1,2,...,n} define maxjump(p) = max(p(i) - i); a(n) is sum of maxjumps of all p.

0, 1, 7, 45, 313, 2421, 20833, 198309, 2073793, 23664021, 292834513, 3907994949, 55967406433, 856355084661, 13944569166193, 240803714700069, 4395998055854593, 84596337986326101, 1711691067680320273, 36329581765125539589, 807099012174816776353

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..448

Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour, and Mark Shattuck, Pushes in permutations, J. Comb. Math. Comb. Comp. (2020) Vol. 115, 77-95.

Formula

a(n) = Sum_{k=0..n-1} k*k!*((k+1)^(n-k)-k^(n-k)).

a(n) = Sum_{k=0..n*(n-1)/2} k*A127452(n-1,k). - Paul D. Hanna, Jan 15 2007

a(n) = Sum_{k=0..n-1} k * A180190(n,k). - Alois P. Heinz, Feb 21 2019

Mathematica

Table[Sum[k*k!*((k+1)^(n-k)-k^(n-k)), {k, 0, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Mar 17 2014 *)

Crossrefs

Cf. A056151, A127452, A130153, A180190.

Sequence in context: A143835 A103719 A134437 * A001266 A071971 A370253

Adjacent sequences: A018924 A018925 A018926 * A018928 A018929 A018930

Keyword

nonn

Author

Emeric Deutsch

Status

approved