A144092 - OEIS

%I #2 Mar 30 2012 18:59:21

%S 1,1,1,1,0,1,1,-1,1,1,1,0,2,0,1,1,1,2,-4,2,1,1,0,3,0,10,0,1,1,-1,3,9,

%T 15,-25,5,1,1,0,4,0,42,0,70,0,1,1,1,4,-16,56,196,196,-196,14,1,1,0,5,

%U 0,120,0,1176

%N Triangle of Hankel transforms of sequence array of C(n,floor(n/2))

%C The parity matrix A144093 of this array seems to have row sums A061338(n+1).

%F Triangle (-1)^C(k+1,2)*H(n,k) where the k-th column of H(n,k) is the Hankel transform of the k-th column of the array [k<=n]*C(n-k,floor((n-k)/2).

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 0, 1,

%e 1, -1, 1, 1,

%e 1, 0, 2, 0, 1,

%e 1, 1, 2, -4, 2, 1,

%e 1, 0, 3, 0, 10, 0, 1,

%e 1, -1, 3, 9, 15, -25, 5, 1,

%e 1, 0, 4, 0, 42, 0, 70, 0, 1,

%e 1, 1, 4, -16, 56, 196, 196, -196, 14, 1,

%e 1, 0, 5, 0, 120, 0, 1176, 0, 588, 0, 1

%K easy,sign,tabl

%O 0,13

%A _Paul Barry_, Sep 10 2008