A239914 Total number of preferential arrangements of 1, 2, ..., n things.

1, 4, 17, 92, 633, 5316, 52609, 598444, 7685705, 109933268, 1732565841, 29824133436, 556682481817, 11198025452260, 241481216430113, 5557135898411468, 135927902927547369, 3521462566184392692, 96323049885512803825, 2774010846129897006940, 83898835844633970888761

Offset: 1

Author

N. J. A. Sloane, Apr 12 2014

Keywords

• nonn

Comments

Although A217389 = a(n)+1 already exists, it is this sequence that one really needs.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..424

Crossrefs

Cf. A000670, A217389.

Programs

Maple

b:= proc(n, k) option remember;
     `if`(n=0, k!, k*b(n-1, k)+b(n-1, k+1))
    end:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n, 0)) end:
seq(a(n), n=1..23);  # Alois P. Heinz, Feb 20 2025

Formula

a(n) = Sum_{k=1..n} A000670(k).

a(n) = A217389(n) - 1.