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

Author

Emeric Deutsch

Keywords

• nonn

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.

Crossrefs

Cf. A056151, A127452, A130153, A180190.

Programs

Mathematica

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

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