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A124645 Triangle T(n,k), 0<=k<=n, read by rows given by [1,-1,0,0,0,0,0,...] DELTA [ -1,2,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . 2
1, 1, -1, 0, 1, -1, 0, 1, -2, 1, 0, 0, 1, -2, 1, 0, 0, 1, -3, 3, -1, 0, 0, 0, 1, -3, 3, -1, 0, 0, 0, 1, -4, 6, -4, 1, 0, 0, 0, 0, 1, -4, 6, -4, 1, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1, 0, 0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Matrix inverse of A108299.

LINKS

Table of n, a(n) for n=0..90.

FORMULA

Row n has g.f.: x^[n/2]*(1-x)^(n-[n/2]).

G.f.: (1-x*y+x)/(1-x^2*y+x^2*y^2). - R. J. Mathar, Aug 11 2015

EXAMPLE

Triangle begins:

1;

1, -1;

0, 1, -1;

0, 1, -2, 1;

0, 0, 1, -2, 1;

0, 0, 1, -3, 3, -1;

0, 0, 0, 1, -3, 3, -1;

0, 0, 0, 1, -4, 6, -4, 1;

0, 0, 0, 0, 1, -4, 6, -4, 1;

0, 0, 0, 0, 1, -5, 10, -10, 5, -1;

0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1;

0, 0, 0, 0, 0, 1, -6, 15, -20, 15, -6, 1 ;...

CROSSREFS

Sequence in context: A281243 A284314 A280454 * A029409 A014674 A015339

Adjacent sequences:  A124642 A124643 A124644 * A124646 A124647 A124648

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Jun 13 2007, Aug 22 2007

STATUS

approved

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Last modified May 26 02:35 EDT 2019. Contains 323579 sequences. (Running on oeis4.)