A220399 - OEIS

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

%S 1,0,1,0,2,1,0,3,4,1,0,3,10,6,1,0,0,18,21,8,1,0,-9,21,53,36,10,1,0,

%T -27,0,99,116,55,12,1,0,-54,-81,117,286,215,78,14,1,0,-81,-270,-27,

%U 528,650,358,105,16,1

%N A convolution triangle of numbers obtained from A057682.

%C Triangle T(n,k) given by (0, 2, -1/2, 3/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

%F G.f.: (1-3*x+3*x^2)/(1-3*x-3*x*y+3*x^2+x^2*y)

%F G.f for k-th column: ((x-x^2)/(1-3*x+3*x^2))^k.

%F T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - T(n-2,k-1), T(0,0) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k<0 or if k>n.

%F Sum_{k, 0<=k<=n, n>0} T(n,k) = A001792(n-1).

%F T(n+1,n) = 2*n = A005843(n).

%F T(n+2,n) = A014105(n).

%F T(n,1) = A057682(n).

%e Triangle begins :

%e 1

%e 0, 1

%e 0, 2, 1

%e 0, 3, 4, 1

%e 0, 3, 10, 6, 1

%e 0, 0, 18, 21, 8, 1

%e 0, -9, 21, 53, 36, 10, 1

%e 0, -27, 0, 99, 116, 55, 12, 1

%Y Cf. A030523, A057682, A104597

%K sign,tabl

%O 0,5

%A _Philippe Deléham_, Feb 19 2013