A131103 - OEIS

A131103

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 no boxes with exactly one object (n, k >= 1).

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

%S 0,0,1,0,2,1,0,3,2,1,0,4,3,8,1,0,5,4,21,22,1,0,6,5,40,63,52,1,0,7,6,

%T 65,124,243,114,1,0,8,7,96,205,664,969,240,1,0,9,8,133,306,1405,3196,

%U 3657,494,1,0,10,9,176,427,2556,7425,15712,12987,1004,1,0,11,10,225,568,4207

%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 are no boxes with exactly one object (n, k >= 1).

%C Problem suggested by Brandon Zeidler. Columns four and five are A000567 and A051874. Second row is A130102.

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

%e Array begins:

%e 0 1 1 1 1 1 1

%e 0 2 2 8 22 52 114

%e 0 3 3 21 63 243 969

%Y Cf. A131104, A131105, A131106, A131107.

%K easy,nonn,tabl

%O 1,5

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