A228997 Total sum of the 7th powers of lengths of ascending runs in all permutations of [n].

0, 1, 130, 2706, 32226, 315684, 2961498, 28544040, 291590754, 3194874900, 37656861354, 477018980928, 6477756701010, 94006723773564, 1453236561824250, 23855684885059944, 414605141516228418, 7607828522859788580, 147012653519046471114, 2984603478905797978320

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=7 of A229001.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, [0, 1, 130, 2706][n+1],
      ((16*n^3-38*n^2-16*n+278) *a(n-1)
      -(8*n^4-3*n^3-101*n^2+623*n-512) *a(n-2)
      +2*(n-2)*(8*n^3-32*n^2+134*n-95) *a(n-3)
      -(n-2)*(n-3)*(8*n^2-37*n+44) *a(n-4)) /(8*n^2-27*n+24))
    end:
seq(a(n), n=0..30);

Mathematica

With[{nn=20},CoefficientList[Series[(Exp[x](42x^5+210x^4+280x^3+126x-126)+x+126)/(x-1)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 31 2021 *)

Formula

E.g.f.: (exp(x)*(42*x^5+210*x^4+280*x^3+126*x-126)+x+126)/(x-1)^2.

a(n) ~ n! * (532*exp(1)+127)*n. - Vaclav Kotesovec, Sep 12 2013