

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
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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)^(nj)C(n,j)C(j+1,k+1)C(j,k)}
T(n,k) = C(n,k)*C(k+1,nk). 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



