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A112475 Riordan array (1/(1+x),x(1+x)/(1-x)). 2

%I #10 Nov 26 2013 13:54:43

%S 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,

%T 11,41,63,41,11,1,1,1,13,61,129,129,61,13,1,-1,1,15,85,231,321,231,85,

%U 15,1,1,1,17,113,377,681,681,377,113,17,1

%N Riordan array (1/(1+x),x(1+x)/(1-x)).

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

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

%e Triangle starts:

%e 1;

%e -1, 1;

%e 1, 1, 1;

%e -1, 1, 3, 1;

%e 1, 1, 5, 5, 1;

%e -1, 1, 7, 13, 7, 1;

%e 1, 1, 9, 25, 25, 9, 1;

%K easy,sign,tabl

%O 0,9

%A _Paul Barry_, Sep 07 2005

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)