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

0,5

Comments

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

Links

Table of n, a(n) for n=0..52.

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

Example

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.

Sequence in context: A290724 A283879 A216178 * A223856 A153661 A266392

Adjacent sequences: A122896 A122897 A122898 * A122900 A122901 A122902

Keyword

easy,nonn,tabl

Author

Paul Barry, Sep 18 2006

Status

approved