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A112475 Riordan array (1/(1+x),x(1+x)/(1-x)). 2
1, -1, 1, 1, 1, 1, -1, 1, 3, 1, 1, 1, 5, 5, 1, -1, 1, 7, 13, 7, 1, 1, 1, 9, 25, 25, 9, 1, -1, 1, 11, 41, 63, 41, 11, 1, 1, 1, 13, 61, 129, 129, 61, 13, 1, -1, 1, 15, 85, 231, 321, 231, 85, 15, 1, 1, 1, 17, 113, 377, 681, 681, 377, 113, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

Equivalent to Delannoy triangle A008288 with prepended column 1,-1,1,-1,... Row sums are A111954. Diagonal sums are A112476. Inverse is A112477.

LINKS

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

FORMULA

Number triangle T(n,k) = Sum{j=0..n-k} C(k-1,j) C(n-j-1,n-k-j).

EXAMPLE

Triangle starts:

   1;

  -1, 1;

   1, 1, 1;

  -1, 1, 3,  1;

   1, 1, 5,  5,  1;

  -1, 1, 7, 13,  7, 1;

   1, 1, 9, 25, 25, 9, 1;

CROSSREFS

Sequence in context: A046643 A254101 A277604 * A307855 A300853 A293012

Adjacent sequences:  A112472 A112473 A112474 * A112476 A112477 A112478

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Sep 07 2005

STATUS

approved

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Last modified June 7 01:26 EDT 2020. Contains 334836 sequences. (Running on oeis4.)