A100822 Triangle read by rows: T(n,k) is the number of deco polyominoes of height n with k cells in the first column. (A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column).

1, 1, 1, 2, 3, 1, 6, 8, 9, 1, 24, 30, 32, 33, 1, 120, 144, 150, 152, 153, 1, 720, 840, 864, 870, 872, 873, 1, 5040, 5760, 5880, 5904, 5910, 5912, 5913, 1, 40320, 45360, 46080, 46200, 46224, 46230, 46232, 46233, 1, 362880, 403200, 408240, 408960, 409080, 409104, 409110, 409112, 409113, 1

Offset: 1

Author

Emeric Deutsch, Jan 06 2005, Aug 09 2006

Keywords

• nonn
• tabl

Comments

Row n has n terms. Rows are circular permutations of the rows of A054115. Column 1 and row sums yield A000142 (the factorial numbers). Column 2 yields A059171.

T(n+1,n)=A007489(n).

Examples

			Triangle begins:
1;
1,1;
2,3,1;
6,8,9,1;
24,30,32,33,1;
T(2,1)=T(2,2)=1 because the deco polyominoes of height 2 are the horizontal and vertical dominoes, having, respectively, 1 and 2 cells in their first columns.
		

References

• E. Barcucci, A. del Lungo and R. Pinzani, "Deco" polyominoes, permutations and random generation, Theoretical Computer Science, 159, 1996, 29-42.

Crossrefs

Cf. A000142, A054115, A059171, A007489.

Programs

Maple

T:=proc(n,k) if k=n then 1 elif k
				

Formula

T(n, k)=sum((n-j)!, j=1..k) for 1<=k

T(n,k)=T(n-1,k-1)+(n-1)! for k

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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