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Weight array of A000007 (which has only one nonzero term and whose second accumulation array is the multiplication table for the positive integers), by antidiagonals.
4

%I #11 Jul 28 2015 05:50:56

%S 1,-1,-1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Weight array of A000007 (which has only one nonzero term and whose second accumulation array is the multiplication table for the positive integers), by antidiagonals.

%C A member of the accumulation chain

%C ... < A185906 < A000007 < A000012 < A003991 < A098358 < A185904 < A185905 < ..., which includes the multiplication table of the positive integers. (See A144112 for the definitions of weight array and accumulation array.)

%F T(1,1)=T(2,2)=1; T(1,2)=T(2,1)=-1; T(n,k)=0 for all other (n,k).

%F a(n) = (1-(-1)^(2^abs((n*(n-1)*(n-2)*(n-3)*(n-5)))))/2*(-1)^((2*n-1+(-1)^n)/4). - _Luce ETIENNE_, Jul 09 2015

%F a(n) = (-1)^floor(n/2)*sign(floor(5/n))-floor(n/4)*floor(4/n). - _Wesley Ivan Hurt_, Jul 10 2015

%e Northwest corner:

%e .1....-1....0....0....0....0....0

%e -1.....1....0....0....0....0....0

%e .0.....0....0....0....0....0....0

%e .0.....0....0....0....0....0....0

%p A185906:=n->(-1)^floor(n/2)*signum(floor(5/n))-floor(n/4)*floor(4/n): seq(A185906(n), n=1..300); # _Wesley Ivan Hurt_, Jul 10 2015

%Y Cf. A144112, A000007.

%K tabl,sign

%O 1

%A _Clark Kimberling_, Feb 06 2011