Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Mar 30 2012 18:59:12
%S 1,-1,1,-1,-2,1,3,-1,-3,1,1,8,0,-4,1,-9,-3,14,2,-5,1,1,-26,-15,20,5,
%T -6,1,27,27,-45,-37,25,9,-7,1,-13,76,98,-56,-70,28,14,-8,1,-81,-135,
%U 108,228,-46,-114,28,20,-9,1,67,-202,-459,48,420,0,-168,24,27,-10,1,243,567,-135,-1035,-210,662,98,-230,15,35,-11,1,-285
%N Inverse of renewal array for central trinomial numbers.
%C Row sums have g.f. 1/sqrt(1+4x^2) [alternating sign central binomial numbers with interpolated zeros]. Diagonal sums are A111964. Inverse of A111960. Factors as (1/sqrt(1+4x^2),x/sqrt(1+4x^2))*(1/(1+x),x/(1+x)).
%F Riordan array (1/(sqrt(1+4x^2)+x), x/(sqrt(1+4x^2)+x)); Number triangle T(n, k)=sum{i=0..floor(n/2), C(2i+k-n-1, k)*C((2i-n-1)/2, i)(-1)^n*4^i}.
%e Triangle begins
%e 1;
%e -1,1;
%e -1,-2,1;
%e 3,-1,-3,1;
%e 1,8,0,-4,1;
%e -9,-3,14,2,-5,1;
%e 1,-26,-15,20,5,-6,1;
%K easy,sign,tabl
%O 0,5
%A _Paul Barry_, Aug 23 2005