A202847 - OEIS

%I #18 Mar 05 2013 15:26:07

%S 1,-1,1,2,-2,1,-3,5,-3,1,6,-10,9,-4,1,-10,22,-22,14,-5,1,20,-44,54,

%T -40,20,-6,1,-35,93,-123,109,-65,27,-7,1,70,-186,281,-276,195,-98,35,

%U -8,1,-126,386,-618,682,-541,321,-140,44,-9,1

%N Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126930.

%F T(n,k) = (-1)^(n-k)*A054336(n,k).

%F Sum_{k, 0<=k<=n}T(n,k)*x^k = (-1)^n*A126931(n), (-1)^n*A054341(n), A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively.

%e Triangle begins

%e 1

%e -1, 1

%e 2, -2, 1

%e -3, 5, -3, 1

%e 6, -10, 9, -4, 1

%e -10, 22, -22, 14, -5, 1

%e 20, -44, 54, -40, 20, -6, 1

%e -35, 93, -123, 109, -65, 27, -7, 1

%e ...

%e Production matrix begins

%e x, 1

%e 1, x, 1

%e 1, 1, x, 1

%e 1, 1, 1, x, 1

%e 1, 1, 1, 1, x, 1

%e 1, 1, 1, 1, 1, x, 1

%e 1, 1, 1, 1, 1, 1, x, 1

%e 1, 1, 1, 1, 1, 1, 1, x, 1

%e 1, 1, 1, 1, 1, 1, 1, 1, x, 1

%e 1, 1, 1, 1, 1, 1, 1, 1, 1, x, 1

%e ..., with x = -1.

%Y Cf. (sequences with similar production matrix) A097609 (x=0), A033184 (x=1), A104259 (x=2), A171568 (x=3), A171589 (x=4)

%K sign,tabl

%O 0,4

%A _Philippe Deléham_, Mar 02 2013