A228996 Total sum of the 6th powers of lengths of ascending runs in all permutations of [n].

0, 1, 66, 992, 9846, 86782, 765506, 7112202, 71000398, 766053422, 8931231882, 112221527986, 1514394506102, 21867699419238, 336675784490002, 5508056657818442, 95455624774115166, 1747299831395273182, 33693372749353108058, 682771622138237836962

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

Column k=6 of A229001.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [0, 1, 66][n+1],
      ((30*n^5-225*n^4+690*n^3-975*n^2+512*n+31)*a(n-1)
      -(n-1)*(15*n^5-90*n^4+255*n^3-330*n^2+121*n+62)*a(n-2)
      +(15*n^6-105*n^5+315*n^4-525*n^3+511*n^2-273*n+62)*a(n-3))/
      (15*n^4-120*n^3+375*n^2-540*n+301))
    end:
seq(a(n), n=0..30);

Formula

E.g.f.: (exp(x)*(30*x^4+60*x^3+60*x^2-60*x+62)-x-62)/(x-1)^2.

a(n) ~ n! * (152*exp(1)-63)*n. - Vaclav Kotesovec, Sep 12 2013