%I #21 Sep 14 2022 16:16:22
%S 0,1,7,45,313,2421,20833,198309,2073793,23664021,292834513,3907994949,
%T 55967406433,856355084661,13944569166193,240803714700069,
%U 4395998055854593,84596337986326101,1711691067680320273,36329581765125539589,807099012174816776353
%N For each permutation p of {1,2,...,n} define maxjump(p) = max(p(i) - i); a(n) is sum of maxjumps of all p.
%H Alois P. Heinz, <a href="/A018927/b018927.txt">Table of n, a(n) for n = 1..448</a>
%H Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour, and Mark Shattuck, <a href="https://www.researchgate.net/profile/Mark-Shattuck/publication/363261940_Pushes_in_permutations/">Pushes in permutations</a>, J. Comb. Math. Comb. Comp. (2020) Vol. 115, 77-95.
%F a(n) = Sum_{k=0..n-1} k*k!*((k+1)^(n-k)-k^(n-k)).
%F a(n) = Sum_{k=0..n*(n-1)/2} k*A127452(n-1,k). - _Paul D. Hanna_, Jan 15 2007
%F a(n) = Sum_{k=0..n-1} k * A180190(n,k). - _Alois P. Heinz_, Feb 21 2019
%t Table[Sum[k*k!*((k+1)^(n-k)-k^(n-k)),{k,0,n-1}],{n,1,20}] (* _Vaclav Kotesovec_, Mar 17 2014 *)
%Y Cf. A056151, A127452, A130153, A180190.
%K nonn
%O 1,3
%A _Emeric Deutsch_