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A117179 Riordan array ((1-x^2)/(1+x^2)^2,x/(1+x^2)). 2
1, 0, 1, -3, 0, 1, 0, -4, 0, 1, 5, 0, -5, 0, 1, 0, 9, 0, -6, 0, 1, -7, 0, 14, 0, -7, 0, 1, 0, -16, 0, 20, 0, -8, 0, 1, 9, 0, -30, 0, 27, 0, -9, 0, 1, 0, 25, 0, -50, 0, 35, 0, -10, 0, 1, -11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Inverse is A117178. Row sums are (-1)^n*A098554(n+1). Diagonal sums are 1,0,-2,0,2,0,-2,... with g.f. (1-x^2)/(1+x^2).

Apparently, with the rows de-aerated and then reversed, this matrix becomes signed A034807 with the twos on the diagonal removed. Apparently, |D(2n,k+1)| = |D(2(n-1),k+1)| + |D(2n,k)| where D(n,k) is the k-th element on the n-th diagonal. - Tom Copeland, May 30 2017

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Triangle begins

1,

0, 1,

-3, 0, 1,

0, -4, 0, 1,

5, 0, -5, 0, 1,

0, 9, 0, -6, 0, 1,

-7, 0, 14, 0, -7, 0, 1,

0, -16, 0, 20, 0, -8, 0, 1

CROSSREFS

Sequence in context: A284148 A108197 A049769 * A111526 A117178 A111527

Adjacent sequences:  A117176 A117177 A117178 * A117180 A117181 A117182

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Mar 01 2006

STATUS

approved

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Last modified February 23 07:47 EST 2018. Contains 299473 sequences. (Running on oeis4.)