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A229002 Total sum of the n-th powers of lengths of ascending runs in all permutations of [n]. 2
0, 1, 6, 66, 1110, 25620, 765506, 28544040, 1293790126, 69860663220, 4422094936842, 323816329558128, 27127369640967206, 2575241880204602700, 274755427187762475922, 32708158728316937527944, 4316964980670466411606110, 628131523035069583394938980 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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);

CROSSREFS

Main diagonal of A229001.

Sequence in context: A112942 A113390 A267080 * A122020 A262601 A329930

Adjacent sequences:  A228999 A229000 A229001 * A229003 A229004 A229005

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 10 2013

STATUS

approved

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Last modified October 29 19:16 EDT 2020. Contains 338067 sequences. (Running on oeis4.)