OFFSET
0,6
COMMENTS
REFERENCES
John J. Watkins, Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, 2004, chapter 7.
LINKS
Alois P. Heinz, Rows n = 0..32, flattened
Stephan Mertens, Domination Polynomial of the Rook Graph, Journal of Integer Sequences 27 (2024), Article 24.3.7; arXiv:2401.00716 [math.CO], 2024.
Eric Weisstein's World of Mathematics, Dominating Set.
Eric Weisstein's World of Mathematics, Rook Graph.
FORMULA
G.f.: ((x+1)^n - 1)^m - (-1)^m * Sum_{k=0..m-1} binomial(m,k)*(-1)^k*((1+x)^k - 1)^n (for the rectangular n X m rook graph).
T(n,n) = 2*n^n - n!.
EXAMPLE
Triangle begins: (first 5 rows)
1;
0,1;
0,0,6,4,1;
0,0,0,48,117,126,84,36,9,1;
0,0,0,0,488,2640,6712,10864,12726,11424,8008,4368,1820,560,120,16,1;
...
MATHEMATICA
R[n_, m_] := CoefficientList[((x + 1)^n - 1)^m - (-1)^m*Sum[Binomial[m, k]*(-1)^k*((1 + x)^k - 1)^n, {k, 0, m - 1}], x];
Flatten[Table[R[n, n], {n, 1, 5}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Stephan Mertens, Jan 07 2024
STATUS
approved