0,9

Inverse is Riordan array (1, xc(x)) (A106566).

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.

Modulo 2, this sequence gives A106344. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2008]

Coefficient array of the polynomials Chebyshev_U(n, sqrt(x)/2)*(sqrt(x))^n. [From Paul Barry (pbarry(AT)wit.ie), Sep 28 2009]

Number triangle T(n, k) = (-1)^(n-k)*binomial(k, n-k).

T(n, k)*2^(n-k) = A110509(n, k); T(n, k)*3^(n-k) = A110517(n, k).

Sum_{k, 0<=k<=n}T(n,k)*A000108(k)=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 11 2007

Sum_{k, 0<=k<=n}T(n,k)*A144706(k)=A082505(n+1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

Sum_{k, 0<=k<=n}T(n,k)*A002450(k)=A100335(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

Sum_{k, 0<=k<=n}T(n,k)*A001906(k)=A100334(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

Sum_{k, 0<=k<=n}T(n,k)*A015565(k)=A099322(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

Sum_{k, 0<=k<=n}T(n,k)*A003462(k)=A106233(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2008]

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]

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]

Rows begin:

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, 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;

Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 28 2009: (Start)

Production array is

0, 1,

0, -1, 1,

0, -1, -1, 1,

0, -2, -1, -1, 1,

0, -5, -2, -1, -1, 1,

0, -14, -5, -2, -1, -1, 1,

0, -42, -14, -5, -2, -1, -1, 1,

0, -132, -42, -14, -5, -2, -1, -1, 1,

0, -429, -132, -42, -14, -5, -2, -1, -1, 1 (End)

Cf. : A026729 (unsigned version).

Adjacent sequences: A109463 A109464 A109465 this_sequence A109467 A109468 A109469

Sequence in context: A108063 A164846 A026729 this_sequence A076833 A071676 A115363

easy,sign,tabl

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 28 2005