A286175 Sum of the n-th entries in all cycles of all permutations of [n+1].

4, 13, 43, 192, 1068, 7080, 54360, 473760, 4616640, 49714560, 586051200, 7504358400, 103703846400, 1538074137600, 24366332390400, 410609751552000, 7333437855744000, 138362409529344000, 2749819506610176000, 57416487392968704000, 1256593887223234560000

Offset: 1

Author

Alois P. Heinz, May 03 2017

Keywords

• nonn

Examples

			a(2) = 13 because the sum of the second entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 2+3+2+3+3+0 = 13.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..448

Crossrefs

Cf. A285793.

Programs

Maple

a:= proc(n) option remember; `if`(n<3, [4, 13][n],
      (n-1)*(2*n^2+7*n+4)*a(n-1)/(2*n^2+3*n-1))
    end:
seq(a(n), n=1..25);

Mathematica

a[n_] := a[n] = If[n < 3, {4, 13}[[n]],
     (n-1)*(2*n^2 + 7*n + 4)*a[n-1]/(2*n^2 + 3*n - 1)];
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Apr 21 2022, after Alois P. Heinz *)

Formula

E.g.f.: -2*log(1-x)-(5*x^3-10*x^2+10*x-7)/(2*(1-x)^2)-7/2.

a(n) = A285793(n+1,n).