A144225 Bordered Pascal's triangle in rectangular format.

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 3, 3, 1, 0, 0, 1, 4, 6, 4, 1, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 1, 7, 21, 35, 35, 21, 7, 1, 0, 0, 1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 1, 10, 45, 120, 210, 252, 210, 120, 45

Offset: 1

Author

Clark Kimberling, Sep 15 2008

Keywords

• nonn
• tabl

Comments

This is the weight array (defined at A144112) of Pascal's rectangle - that is, Pascal's triangle A007318 formatted as a rectangle.

Examples

			Northwest corner:
1 0 0 0 0 0 0 0
0 1 1 1 1 1 1 1
0 1 2 3 4 5 6 7
0 1 3 6 10 15 21 28
0 1 4 10 20 35 56
		

Crossrefs

A007318, A144112.

Formula

After deleting row 1, (1 0 0 0 ...) and column 1, (1 0 0 0 ...), the remaining array is given by R(m,n)=C(m+n-2,m-1). This "Pascal rectangle" is the accumulation array of A144225.