|
%I #9 Sep 11 2013 20:19:44
%S 0,1,6,66,1110,25620,765506,28544040,1293790126,69860663220,
%T 4422094936842,323816329558128,27127369640967206,2575241880204602700,
%U 274755427187762475922,32708158728316937527944,4316964980670466411606110,628131523035069583394938980
%N Total sum of the n-th powers of lengths of ascending runs in all permutations of [n].
%H Alois P. Heinz, <a href="/A229002/b229002.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=1..n} k^n * A122843(n,k).
%p a:= n-> add(`if`(n=k, 1, n!/(k+1)!*(k*(n-k+1)+1
%p -((k+1)*(n-k)+1)/(k+2)))*k^n, k=1..n):
%p seq(a(n), n=1..20);
%Y Main diagonal of A229001.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Sep 10 2013
|
