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

1,13

Comments

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

Links

Table of n, a(n) for n=1..88.

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.

Example

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.

Sequence in context: A327191 A036867 A036866 * A159854 A127840 A017837

Adjacent sequences: A144222 A144223 A144224 * A144226 A144227 A144228

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 15 2008

Status

approved