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A122899
Triangle with row sums counting directed animals.
3
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.
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
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Sep 18 2006
STATUS
approved