A131104 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 is one box with exactly one object (n, k >= 1).

1, 2, 0, 3, 0, 0, 4, 0, 6, 0, 5, 0, 18, 8, 0, 6, 0, 36, 24, 10, 0, 7, 0, 60, 48, 120, 12, 0, 8, 0, 90, 80, 420, 396, 14, 0, 9, 0, 126, 120, 1000, 1512, 1092, 16, 0, 10, 0, 168, 168, 1950, 3720, 6804, 2736, 18, 0, 11, 0, 216, 224, 3360, 7380, 23240, 31008, 6480, 20, 0, 12, 0

Offset: 1

Author

David Wasserman, Jun 14 2007, Jun 15 2007

Keywords

• easy
• nonn
• tabl

Comments

Problem suggested by Brandon Zeidler. Columns 3 through 5 are A028896, A033996, 10*A007586.

Examples

			Array begins:
1 0 0 0 0 0 0
2 0 6 8 10 12 14
3 0 18 24 120 396 1092
		

Crossrefs

Cf. A131103, A131105, A131106, A131107.

Formula

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