A229003 Total sum of cubed lengths of ascending runs in all permutations of [n].

0, 1, 10, 66, 426, 2964, 22818, 195000, 1842234, 19120260, 216604194, 2662063728, 35297775930, 502460232684, 7644691295970, 123824090015544, 2127644969464698, 38659776477571860, 740692592536389474, 14924674961053224000, 315523813278300959994

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=3 of A229001.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [0, 1, 10][n+1],
      ((2*n^2-3*n-1)*a(n-1) -(n-1)*(n^2-2)*a(n-2)
       +(n-2)*(n-1)^2*a(n-3) )/(n-2))
    end:
seq(a(n), n=0..25);

Mathematica

With[{nn=20},CoefficientList[Series[(6 Exp[x](x-1)+x+6)/(x-1)^2,{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Aug 26 2019 *)

Formula

E.g.f.: (6*exp(x)*(x-1)+x+6)/(x-1)^2.

a(n) ~ n! * 7*n. - Vaclav Kotesovec, Sep 12 2013