A131105 Rectangular array read by antidiagonals: a(n, k) is the number of ways to put k labeled objects into n labeled boxes so that there are exactly two boxes with exactly one object (n, k >= 2).

2, 6, 0, 12, 0, 0, 20, 0, 36, 0, 30, 0, 144, 60, 0, 42, 0, 360, 240, 90, 0, 56, 0, 720, 600, 1440, 126, 0, 72, 0, 1260, 1200, 6300, 5544, 168, 0, 90, 0, 2016, 2100, 18000, 26460, 17472, 216, 0, 110, 0, 3024, 3360, 40950, 78120, 136080, 49248, 270, 0, 132, 0, 4320

Offset: 2

Author

David Wasserman, Jun 15 2007

Keywords

• easy
• nonn
• tabl

Comments

Problem suggested by Brandon Zeidler. Columns 2, 4 and 5 are A002378, 36*A000292 and 60*A000292.

Examples

			Array begins:
2 0 0 0 0 0
6 0 36 60 90 126
12 0 144 240 1440 5544
		

Crossrefs

Cf. A131103, A131104, A131106, A131107.

Formula

a(n, 2) = n^2-n. For k > 2, a(n, k) = sum_{j=1..min(floor(k/2)-1, n-2)} A008299(k-2, j)*n!*(k^2-k)/(2*(n-j-2)!).