%I
%S 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,
%T 0,35,350,315,49,1,0,0,0,0,350,1120,588,64,1,0,0,0,0,126,1890,2940,
%U 1008
%N Triangle with row sums counting directed animals.
%C Row sums are A005773(n+1). Product of A007318 and A122899 is A103371.
%F Number triangle T(n,k)=sum{j=0..n, (1)^(nj)C(n,j)C(j+1,k+1)C(j,k)}
%F 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
%e Triangle begins
%e 1,
%e 1, 1,
%e 0, 4, 1,
%e 0, 3, 9, 1,
%e 0, 0, 18, 16, 1,
%e 0, 0, 10, 60, 25, 1,
%e 0, 0, 0, 80, 150, 36, 1,
%e 0, 0, 0, 35, 350, 315, 49, 1,
%e 0, 0, 0, 0, 350, 1120, 588, 64, 1,
%e 0, 0, 0, 0, 126, 1890, 2940, 1008, 81, 1,
%e 0, 0, 0, 0, 0, 1512, 7350, 6720, 1620, 100, 1
%Y Cf. A123160.
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Sep 18 2006
