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%I #5 Mar 31 2012 13:20:06
%S 1,1,1,1,1,1,5,-10,10,-5,1,4,-5,0,5,-4,1,3,0,-10,15,-9,2,2,5,-20,25,
%T -14,3,1,10,-30,35,-19,4,15,-40,45,-24,5,10,-5,-65,181,-246,210,-120,
%U 45,-10,1,6,20,-130,266,-287,168,-30,-30,25,-8,1
%N Coefficient array for certain numerator polynomials N6(n,x), n >= 0 (rising powers of x).
%C The g.f. of column k of array A063260(n,k) (sextinomial coefficients) is (x^(ceiling(k/5)))*N6(k,x)/(1-x)^(k+1).
%C The sequence of degrees for the polynomials N6(n,x) is [0,0,0,0,0,0,4,5,5,5,5,4,9,10,10,...] for n >= 0.
%C Row sums N6(n,1)=1 for all n.
%F a(n, m) = [x^m]N6(n, x), n, m >= 0, with N6(n, x)= sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N6(n-j, x), j=1..5), N6(n, x)= 1 for n=0, 1, 2, 3, 4 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 4 if mod(n, 5)=0 else c(n) := mod(n, 5)-1; (hence b(0, j)=0, j=1..5).
%e {1}; {1}; {1}; {1}; {1}; {1}; {5, -10, 10, -5, 1}; {4, -5, 0, 5, -4, 1}; ...
%e c=2: b(2,1)=b(2,2)=1, b(2,j)=0 for j=3,4,5.
%e N6(7,x)=4-5*x+0*x^2+5*x^3-4*x^4+x^5.
%K sign,easy,tabf
%O 0,7
%A _Wolfdieter Lang_, Jul 24 2001
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