A122899 Triangle with row sums counting directed animals.

1, 1, 1, 0, 4, 1, 0, 3, 9, 1, 0, 0, 18, 16, 1, 0, 0, 10, 60, 25, 1, 0, 0, 0, 80, 150, 36, 1, 0, 0, 0, 35, 350, 315, 49, 1, 0, 0, 0, 0, 350, 1120, 588, 64, 1, 0, 0, 0, 0, 126, 1890, 2940, 1008

Offset: 0

Author

Paul Barry, Sep 18 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A005773(n+1). Product of A007318 and A122899 is A103371.

Examples

			Triangle begins
1,
1, 1,
0, 4, 1,
0, 3, 9, 1,
0, 0, 18, 16, 1,
0, 0, 10, 60, 25, 1,
0, 0, 0, 80, 150, 36, 1,
0, 0, 0, 35, 350, 315, 49, 1,
0, 0, 0, 0, 350, 1120, 588, 64, 1,
0, 0, 0, 0, 126, 1890, 2940, 1008, 81, 1,
0, 0, 0, 0, 0, 1512, 7350, 6720, 1620, 100, 1
		

Crossrefs

Cf. A123160.

Formula

Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)C(j,k)}

T(n,k) = C(n,k)*C(k+1,n-k). The columns of this triangle (ignoring leading zeros) give the rows of A123160. - Peter Bala, Jan 24 2008