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A098599 Riordan array ((1+2x)/(1+x),(1+x)). 7
1, 1, 1, -1, 2, 1, 1, 0, 3, 1, -1, 0, 2, 4, 1, 1, 0, 0, 5, 5, 1, -1, 0, 0, 2, 9, 6, 1, 1, 0, 0, 0, 7, 14, 7, 1, -1, 0, 0, 0, 2, 16, 20, 8, 1, 1, 0, 0, 0, 0, 9, 30, 27, 9, 1, -1, 0, 0, 0, 0, 2, 25, 50, 35, 10, 1, 1, 0, 0, 0, 0, 0, 11, 55, 77, 44, 11, 1, -1, 0, 0, 0, 0, 0, 2, 36, 105, 112, 54, 12, 1, 1, 0, 0, 0, 0, 0, 0, 13, 91, 182, 156, 65, 13, 1, -1, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..109.

FORMULA

Triangle T(n, k) = binomial(k, n-k)+binomial(k-1, n-k-1).

T(n,k) = T(n-1,k-1)-T(n-1,k)+2*T(n-2,k-1)+T(n-3,k-1), T(0,0)=1, T(1,0)=1, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 09 2014

EXAMPLE

Rows begin {1}, {1,1}, {-1,2,1}, {1,0,3,1}, {-1,0,2,4,1},...

CROSSREFS

Row sums are A098600. Diagonal sums are A098601.

Cf. A029635. Apart from signs, same as A100218. Very similar to triangle A111125.

Sequence in context: A175417 A136481 A100218 * A129334 A116399 A116405

Adjacent sequences:  A098596 A098597 A098598 * A098600 A098601 A098602

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Sep 17 2004

STATUS

approved

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Last modified February 20 12:33 EST 2018. Contains 299379 sequences. (Running on oeis4.)