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A176120 Triangle read by rows: Sum_{k=0..min(n,m)} binomial(n,k)*binomial(m,k)*k!. 5
1, 1, 2, 1, 3, 7, 1, 4, 13, 34, 1, 5, 21, 73, 209, 1, 6, 31, 136, 501, 1546, 1, 7, 43, 229, 1045, 4051, 13327, 1, 8, 57, 358, 1961, 9276, 37633, 130922, 1, 9, 73, 529, 3393, 19081, 93289, 394353, 1441729, 1, 10, 91, 748, 5509, 36046, 207775, 1047376 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of ways of placing any number k=0,1,.., min(n,m) of non-attacking rooks on an n X m chessboard. - R. J. Mathar, Dec 19 2014

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

Wikipedia, Rook polynomial

FORMULA

t(n,m) = A088699(n,m). - Peter Bala, Aug 26 2013

t(n,m) = A086885(n,m). - R. J. Mathar, Dec 19 2014

EXAMPLE

1;

1, 2;

1, 3, 7;

1, 4, 13, 34;

1, 5, 21, 73, 209;

1, 6, 31, 136, 501, 1546;

1, 7, 43, 229, 1045, 4051, 13327;

1, 8, 57, 358, 1961, 9276, 37633, 130922;

1, 9, 73, 529, 3393, 19081, 93289, 394353, 1441729;

1, 10, 91, 748, 5509, 36046, 207775, 1047376, 4596553, 17572114;

1, 11, 111, 1021, 8501, 63591, 424051, 2501801, 12975561, 58941091, 234662231;

MAPLE

A176120 := proc(i, j)

        add(binomial(i, k)*binomial(j, k)*k!, k=0..min(i, j)) ;

end proc: # R. J. Mathar, Jul 28 2016

MATHEMATICA

t[n_, m_] = Sum[Binomial[n, k]*Binomial[m, k]*k!, {k, 0, m}];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A086885 (table without column 0), A129833 (row sums).

Cf. A002720.

Sequence in context: A326308 A073901 A116381 * A220621 A058170 A238206

Adjacent sequences:  A176117 A176118 A176119 * A176121 A176122 A176123

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula, Apr 09 2010

STATUS

approved

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Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)