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%I #5 Mar 31 2012 13:20:06
%S 1,1,1,1,1,4,-6,4,-1,3,-2,-2,3,-1,2,2,-8,7,-2,1,6,-14,11,-3,10,-20,15,
%T -4,6,2,-37,65,-56,28,-8,1,3,16,-61,78,-42,0,12,-6,1,1,22,-57,35,42,
%U -84,60,-21,3,20,-25,-64,196,-224,136,-44,6,10,35,-219,420
%N Coefficient array for certain numerator polynomials N5(n,x), n >= 0 (rising powers of x) used for quintinomials (also called pentanomials).
%C The g.f. of column k of array A035343(n,k) (quintinomial coefficients) is (x^(ceiling(k/4)))*N5(k,x)/(1-x)^(k+1).
%C The sequence of degrees for the polynomials N5(n,x) is [0, 0, 0, 0, 0, 3, 4, 4, 4, 3, 7, 8, 8, 7, 7,...] for n >= 0.
%C Row sums N5(n,1)=1 for all n.
%F a(n, m) = [x^m]N5(n, x), n, m >= 0, with N5(n, x)= sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N5(n-j, x), j=1..4), N5(n, x)= 1 for n=0..3 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 3 if mod(n, 4)=0 else c(n) := mod(n, 4)-1; (hence b(0, j)=0, j=1..4).
%e {1}; {1}; {1}; {1}; {1}; {4,-6,4,-1}; {3,-2,-2,3,-1}; {2,2,-8,7,-2}; {1,6,-14,11,-3}; ...
%e c=2: b(2,1)= 1 = b(2,2), b(2,3)= 0 =b(2,4).
%e N5(6,x)=3-2*x-2*x^2+3*x^3-x^4.
%K sign,easy,tabf
%O 0,6
%A _Wolfdieter Lang_, Jul 27 2001
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