A125692 - OEIS

%I #6 Dec 29 2023 11:52:42

%S 1,-1,1,0,-2,1,1,1,-3,1,0,2,3,-4,1,-2,-2,2,6,-5,1,0,-4,-6,0,10,-6,1,5,

%T 5,-3,-11,-5,15,-7,1,0,10,15,4,-15,-14,21,-8,1,-14,-14,6,26,19,-15,

%U -28,28,-9,1,0,-28,-42,-16,30,42,-7,-48,36,-10,1

%N Riordan array (1-x*c(-x^2),x(1-x*c(-x^2))) where c(x) is the g.f. of A000108.

%C Row sums are aerated signed Catalan numbers with g.f. c(-x^2). Inverse of A105306. First column is A105523.

%e Triangle begins

%e 1,

%e -1, 1,

%e 0, -2, 1,

%e 1, 1, -3, 1,

%e 0, 2, 3, -4, 1,

%e -2, -2, 2, 6, -5, 1,

%e 0, -4, -6, 0, 10, -6, 1

%e Contribution from _Paul Barry_, Apr 18 2010: (Start)

%e Production matrix begins

%e -1, 1,

%e -1, -1, 1,

%e -1, -1, -1, 1,

%e -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, -1, -1, -1, -1, 1,

%e -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1 (End)

%K easy,sign,tabl

%O 0,5

%A _Paul Barry_, Nov 30 2006