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%I #12 Oct 14 2017 15:43:33
%S 1,2,2,3,6,3,4,11,11,4,5,18,48,18,5,6,27,109,109,27,6,7,38,218,488,
%T 218,38,7,8,51,405,1409,1409,405,51,8,9,66,724,3832,6130,3832,724,66,
%U 9,10,83,1277,10385,21601,21601,10385,1277,83,10
%N Array read by antidiagonals: T(m,n) = number of minimal dominating sets in the rook graph K_m X K_n.
%H Andrew Howroyd, <a href="/A290632/b290632.txt">Table of n, a(n) for n = 1..1275</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%F T(m, n) = T(n, m).
%F T(n, k) = k^n + n^k - k! * stirling2(n,k) for k<=n.
%e Array begins:
%e ========================================================
%e m\n| 1 2 3 4 5 6 7 8
%e ---|----------------------------------------------------
%e 1 | 1 2 3 4 5 6 7 8 ...
%e 2 | 2 6 11 18 27 38 51 66 ...
%e 3 | 3 11 48 109 218 405 724 1277 ...
%e 4 | 4 18 109 488 1409 3832 10385 28808 ...
%e 5 | 5 27 218 1409 6130 21601 78132 297393 ...
%e 6 | 6 38 405 3832 21601 92592 382465 1750240 ...
%e 7 | 7 51 724 10385 78132 382465 1642046 7720833 ...
%e 8 | 8 66 1277 28808 297393 1750240 7720833 33514112 ...
%e ...
%t T[m_, n_] := m^n + n^m - Min[m, n]! StirlingS2[Max[m, n], Min[m, n]] (* _Eric W. Weisstein_, Aug 10 2017 *)
%o (PARI)
%o T(m,n) = m^n + n^m - if(n<=m, n!*stirling(m,n,2), m!*stirling(n,m,2));
%Y Main diagonal is A248744.
%Y Cf. A287274.
%K nonn,tabl
%O 1,2
%A _Andrew Howroyd_, Aug 07 2017
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