A229002 Total sum of the n-th powers of lengths of ascending runs in all permutations of [n].

0, 1, 6, 66, 1110, 25620, 765506, 28544040, 1293790126, 69860663220, 4422094936842, 323816329558128, 27127369640967206, 2575241880204602700, 274755427187762475922, 32708158728316937527944, 4316964980670466411606110, 628131523035069583394938980

Offset: 0

Author

Alois P. Heinz, Sep 10 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Main diagonal of A229001.

Programs

Maple

a:= n-> add(`if`(n=k, 1, n!/(k+1)!*(k*(n-k+1)+1
        -((k+1)*(n-k)+1)/(k+2)))*k^n, k=1..n):
seq(a(n), n=1..20);

Formula

a(n) = Sum_{k=1..n} k^n * A122843(n,k).