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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).

%I A131105 #4 Mar 30 2012 17:38:08
%S A131105 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,
%T A131105 1440,126,0,72,0,1260,1200,6300,5544,168,0,90,0,2016,2100,18000,26460,
%U A131105 17472,216,0,110,0,3024,3360,40950,78120,136080,49248,270,0,132,0,4320
%N 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).
%C A131105 Problem suggested by Brandon Zeidler. Columns 2, 4 and 5 are A002378, 36*A000292 and 60*A000292.
%F A131105 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)!).
%e A131105 Array begins:
%e A131105 2 0 0 0 0 0
%e A131105 6 0 36 60 90 126
%e A131105 12 0 144 240 1440 5544
%Y A131105 Cf. A131103, A131104, A131106, A131107.
%K A131105 easy,nonn,tabl
%O A131105 2,1
%A A131105 _David Wasserman_, Jun 15 2007