A228994 Total sum of the 4th powers of lengths of ascending runs in all permutations of [n].

0, 1, 18, 152, 1110, 8254, 66050, 578466, 5557246, 58381646, 667481754, 8262618730, 110195259446, 1576108225446, 24075493095346, 391282065519074, 6742907753730030, 122830141805635966, 2358555332361509066, 47617194132209848026, 1008436738991020480294

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=4 of A229001.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [0, 1, 18][n+1],
      ((12*n^3-42*n^2+38*n+7)*a(n-1)-(n-1)*(6*n^3-12*n^2+n+14)*a(n-2)
       +(n-1)*(n-2)*(6*n^2-12*n+7)*a(n-3))/(6*n^2-24*n+25))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := With[{k = 4}, Sum[If[n==t, 1, (n!/(t+1)!)(t(n-t+1)+1-((t+1)(n-t)+1)/(t+2))] t^k, {t, 1, n}]];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz in A229001 *)

Formula

E.g.f.: (exp(x)*(12*x^2-12*x+14)-x-14)/(x-1)^2.

a(n) ~ n! * (14*exp(1)-15)*n. - Vaclav Kotesovec, Sep 12 2013