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A267849
Triangular array: T(n,k) is the 2-row creation rook number to place k rooks on a 3 x n board.
0
1, 1, 3, 1, 6, 12, 1, 9, 36, 60, 1, 12, 72, 240, 360, 1, 15, 120, 600, 1800, 2520, 1, 18, 180, 1200, 5400, 15120, 20160, 1, 21, 252, 2100, 12600, 52920, 141120, 181440, 1, 24, 336, 3360, 25200, 141120, 564480, 1451520, 1814400, 1, 27, 432, 5040, 45360, 317520, 1693440, 6531840, 16329600, 19958400
OFFSET
0,3
COMMENTS
T(n,k) is the number of ways to place k rooks in a 3 x n Ferrers board (or diagram) under the Goldman-Haglund i-row creation rook mode for i=2. All row heights are 3.
LINKS
Jay Goldman and James Haglund, Generalized rook polynomials, J. Combin. Theory A 91 (2000), 509-530.
FORMULA
T(n,k) = T(n-1,k) + (k+2) T(n-1,k-1) subject to T(0,0)=1, T(n,k)=0 for n<k and for k<0.
EXAMPLE
The triangle T(n,k) begins in row n=0 with columns 0<=k<=n:
1
1 3
1 6 12
1 9 36 60
1 12 72 240 360
1 15 120 600 1800 2520
1 18 180 1200 5400 15120 20160
1 21 252 2100 12600 52920 141120 181440
1 24 336 3360 25200 141120 564480 1451520 1814400
1 27 432 5040 45360 317520 1693440 6531840 16329600 19958400
CROSSREFS
Cf. A013610 (1-rook coefficients on the 3xn board), A121757 (2-rook coeffs. on the 2xn board), A013609 (1-rook coeffs. on the 2xn board), A013611 (1-rook coeffs. on the 4xn board), A008279 (2-rook coeffs. on the 1xn board), A082030 (row sums?), A049598 (column k=2), A007531 (column k=3 w/o factor 10), A001710 (diagonal?).
Sequence in context: A110770 A106855 A064282 * A087644 A049964 A143984
KEYWORD
nonn,easy,tabl
AUTHOR
EXTENSIONS
Triangle simplified (reversing rows, offset 0). - R. J. Mathar, May 03 2017
STATUS
approved