A202480 - OEIS

%I #6 Feb 22 2013 14:40:24

%S 1,1,-1,1,-1,1,1,0,1,-1,1,2,-1,-1,1,1,5,-5,2,1,-1,1,9,-10,8,-3,-1,1,1,

%T 14,-14,14,-11,4,1,-1,1,20,-14,14,-17,14,-5,-1,1,1,27,-6,0,-9,19,-17,

%U 6,1,-1

%N Riordan array (1/(1-x), x(2x-1)/(1-x)^2)

%C Row sums are Fibonacci(n-1) = A000045(n-1).

%C Diagonal sums are A078003(n).

%C (Sum_{j, 0<=j<=k} T(k,j))/(1-2x)^k gives g.f. of column A165241(n+k-1,k-1) in triangular array in A165241.

%F T(n,k) = 2*T(n-1,k) + 2*T(n-2,k-1) - T(n-1,k-1) - T(n-2,k).

%F T(n,k) = (-1)^n*A124341(n,k).

%e Triangle begins :

%e 1

%e 1, -1

%e 1, -1, 1

%e 1, 0, 1, -1

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

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

%e 1, 9, -10, 8, -3, -1, 1

%e 1, 14, -14, 14, -11, 4, 1, -1

%e (1+x^2-x^3)/(1-2x)^3 is the g.f of column A165241(n+2,2) := 1, 6, 25, 85, 258, 728, 1952, 5040, ...

%Y Cf. A000012, A080956, A000045, A078003, A124341, A165241

%K easy,sign,tabl

%O 0,12

%A _Philippe Deléham_, Dec 20 2011