A019581 Place n distinguishable balls in n boxes (in n^n ways); let f(n,k) = number of ways that max in any box is k, for 1<=k<=n; sequence gives f(n,2).

0, 2, 18, 180, 2100, 28800, 458640, 8361360, 172141200, 3954484800, 100330876800, 2786980996800, 84133667217600, 2742770705875200, 96032990237184000, 3594185336405664000, 143193231131382432000, 6050494745192177280000, 270263142944131873536000

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Formula

a(n) = sum(d=1..floor(n/2), n!^2 / ( 2^d * (n-2*d)! * d! * d! ) ).

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-j, i-1)/j!, j=0..min(2, n))))
    end:
a:= n-> n! *(b(n$2) -1):
seq(a(n), n=1..30);  # Alois P. Heinz, Jul 29 2014

Mathematica

a[n_] := n! (Hypergeometric2F1[1/2 - n/2, -n/2, 1, 2] - 1); Array[a, 30] (* Jean-François Alcover, Feb 18 2016 *)

Prog

(PARI) a(n) = sum(d=1, n\2, n!^2 / (2^d * (n-2*d)! * d!^2)); \\ Michel Marcus, Aug 13 2013

Crossrefs

Cf. A019576.

Column k=2 of A019575. - Alois P. Heinz, Jul 29 2014

Sequence in context: A337855 A099044 A161122 * A183285 A359458 A129627

Adjacent sequences: A019578 A019579 A019580 * A019582 A019583 A019584

Keyword

nonn,easy

Author

Lee Corbin (lcorbin(AT)tsoft.com), N. J. A. Sloane.

Status

approved