%I A109466
%S A109466 1,0,1,0,1,1,0,0,2,1,0,0,1,3,1,0,0,0,3,4,1,0,0,0,1,6,5,1,0,0,0,0,4,10,
%T A109466 6,1,0,0,0,0,1,10,15,7,1,0,0,0,0,0,5,20,21,8,1,0,0,0,0,0,1,15,35,28,9,
%U A109466 1,0,0,0,0,0,0,6,35,56,36,10,1,0,0,0,0,0,0,1,21,70,84,45,11,1,0,0,0,0
%V A109466 1,0,1,0,-1,1,0,0,-2,1,0,0,1,-3,1,0,0,0,3,-4,1,0,0,0,-1,6,-5,1,0,0,0,0,
               -4,10,-6,1,0,
%W A109466 0,0,0,1,-10,15,-7,1,0,0,0,0,0,5,-20,21,-8,1,0,0,0,0,0,-1,15,-35,28,-9,
               1,0,0,0,0,0,0,
%X A109466 -6,35,-56,36,-10,1,0,0,0,0,0,0,1,-21,70,-84,45,-11,1,0,0,0,0
%N A109466 Riordan array (1, x(1-x)).
%C A109466 Inverse is Riordan array (1, xc(x)) (A106566).
%C A109466 Triangle T(n,k), 0<=k<=n, read by rows, given by [0, -1, 1, 0, 0, 0, 
               0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is 
               the operator defined in A084938.
%C A109466 Modulo 2, this sequence gives A106344. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Dec 18 2008]
%C A109466 Coefficient array of the polynomials Chebyshev_U(n, sqrt(x)/2)*(sqrt(x))^n. 
               [From Paul Barry (pbarry(AT)wit.ie), Sep 28 2009]
%F A109466 Number triangle T(n, k) = (-1)^(n-k)*binomial(k, n-k).
%F A109466 T(n, k)*2^(n-k) = A110509(n, k); T(n, k)*3^(n-k) = A110517(n, k).
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A000108(k)=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jun 11 2007
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A144706(k)=A082505(n+1). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A002450(k)=A100335(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A001906(k)=A100334(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A015565(k)=A099322(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*A003462(k)=A106233(n). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A053404(n), A015447(n), A015446(n), 
               A015445(n), A015443(n), A015442(n), A015441(n), A015440(n), A006131(n), 
               A006130(n), A001045(n+1), A000045(n+1), A000012(n), A010892(n), A107920(n+1), 
               A106852(n), A106853(n), A106854(n), A145934(n), A145976(n), A145978(n), 
               A146078(n), A146080(n), A146083(n), A146084(n) for x = -12,-11,-10,
               -9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11,12 respectively. 
               [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 27 2008]
%F A109466 Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A010892(n), A099087(n), A057083(n), 
               A001787(n+1), A030191(n), A030192(n), A030240(n), A057084(n), A057085(n+1), 
               A057086(n) for x = 0,1,2,3,4,5,6,7,8,9,10 respectively. [From Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2008]
%e A109466 Rows begin:
%e A109466 1;
%e A109466 0, 1;
%e A109466 0, -1, 1;
%e A109466 0, 0, -2, 1;
%e A109466 0, 0, 1, -3, 1;
%e A109466 0, 0, 0, 3, -4, 1;
%e A109466 0, 0, 0, -1, 6, -5, 1;
%e A109466 0, 0, 0, 0, -4, 10, -6, 1;
%e A109466 0, 0, 0, 0, 1, -10, 15, -7, 1;
%e A109466 0, 0, 0, 0, 0, 5, -20, 21, -8, 1;
%e A109466 0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1;
%e A109466 Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 28 2009: (Start)
%e A109466 Production array is
%e A109466 0, 1,
%e A109466 0, -1, 1,
%e A109466 0, -1, -1, 1,
%e A109466 0, -2, -1, -1, 1,
%e A109466 0, -5, -2, -1, -1, 1,
%e A109466 0, -14, -5, -2, -1, -1, 1,
%e A109466 0, -42, -14, -5, -2, -1, -1, 1,
%e A109466 0, -132, -42, -14, -5, -2, -1, -1, 1,
%e A109466 0, -429, -132, -42, -14, -5, -2, -1, -1, 1 (End)
%Y A109466 Cf. : A026729 (unsigned version).
%Y A109466 Sequence in context: A108063 A164846 A026729 this_sequence A076833 A071676 
               A115363
%Y A109466 Adjacent sequences: A109463 A109464 A109465 this_sequence A109467 A109468 
               A109469
%K A109466 easy,sign,tabl
%O A109466 0,9
%A A109466 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 28 2005