%I #6 Mar 31 2012 13:20:06

%S 1,1,1,2,-1,1,1,-1,3,-2,1,3,-4,1,4,-2,-2,1,1,6,-9,3,5,0,-9,6,-1,1,10,

%T -15,3,3,-1,6,5,-24,18,-4,1,15,-20,-6,18,-8,1,7,14,-49,36,-4,-4,1,1,

%U 21,-21,-35,60,-30,5,8,28,-84,50,20,-30,10,-1,1,28,-14

%N Coefficient array for certain numerator polynomials N3(n,x), n >= 0 (rising powers of x) used for trinomials.

%C The g.f. of column k of array A027907(n,k) (trinomial coefficients) is (x^(ceiling(k/2)))*N3(k,x)/(1-x)^(k+1).

%C The sequence of degrees for the polynomials N3(n,x) is [0, 0, 0, 1, 2, 1, 3, 3, 3, 4, 5, 4, 6, 6, 6,...] for n >= 0.

%C Row sums N3(n,1)=1 for all n.

%F a(n, m) = [x^m]N3(n, x), n, m >= 0, with N3(n, x)= sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N3(n-j, x), j=1..2), N3(n, x)= 1 for n=0, 1 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 1 if mod(n, 2)=0 else c(n) := mod(n, 2)-1; (hence b(0, j)=0, j=1..2).

%e {1}; {1}; {1}; {2,-1}; {1,1,-1}; {3,-2}; {1,3,-4,1}; {4,-2,-2,1}; ...

%e c=1: b(1,1)=1, b(1,2)=0.

%e N3(7,x)=4-2*x-2*x^2+5*x^3.

%K sign,easy,tabf

%O 0,4

%A _Wolfdieter Lang_, Jul 27 2001