A221179 - OEIS

%I #14 Feb 22 2013 14:40:40

%S 1,0,1,0,1,1,0,0,2,1,0,-2,1,3,1,0,-4,-4,3,4,1,0,-4,-12,-5,6,5,1,0,0,

%T -16,-24,-4,10,6,1,0,8,-4,-42,-39,0,15,7,1,0,16,32,-24,-88,-55,8,21,8,

%U 1,0,16,80,72,-80

%N A convolution triangle of numbers obtained from A146559.

%C Triangle T(n,k) given by (0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%F G.f. for the k-th column: ((x-x^2)/(1-2*x+2*x^2))^k.

%F G.f.: (1-2*x+2*x^2)/(1-2*x+2*x^2-x*y+x^2*y).

%F T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k) - T(n-2,k-1), T(0,0)=1, T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

%F T(n,k) = (-1)^(n-k)*A181472(n-1,k-1) for n>0 and k>0.

%F T(n,1) = A146559(n-1).

%F T(n+1,n) = n = A001477(n).

%F T(n+2,n) = (n^2-n)/2 = A161680(n).

%F Sum_{k, 0<=k<=n} T(n,k) = A057682(n) for n>0.

%e Triangle begins:

%e 1

%e 0, 1

%e 0, 1, 1

%e 0, 0, 2, 1

%e 0, -2, 1, 3, 1

%e 0, -4, -4, 3, 4, 1

%e 0, -4, -12, -5, 6, 5, 1

%e 0, 0, -16, -24, -4, 10, 6, 1

%Y Cf. A030523, A104597, A181472, A220399

%K sign,tabl

%O 0,9

%A _Philippe Deléham_, Feb 20 2013