A131104 - OEIS

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).

%I #3 Mar 30 2012 17:38:08

%S 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,

%T 90,80,420,396,14,0,9,0,126,120,1000,1512,1092,16,0,10,0,168,168,1950,

%U 3720,6804,2736,18,0,11,0,216,224,3360,7380,23240,31008,6480,20,0,12,0

%N 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).

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

%F 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)!.

%e Array begins:

%e 1 0 0 0 0 0 0

%e 2 0 6 8 10 12 14

%e 3 0 18 24 120 396 1092

%Y Cf. A131103, A131105, A131106, A131107.

%K easy,nonn,tabl

%O 1,2

%A _David Wasserman_, Jun 14 2007, Jun 15 2007