A063261 Coefficient array for certain numerator polynomials N6(n,x), n >= 0 (rising powers of x).

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, -14, 3, 1, 10, -30, 35, -19, 4, 15, -40, 45, -24, 5, 10, -5, -65, 181, -246, 210, -120, 45, -10, 1, 6, 20, -130, 266, -287, 168, -30, -30, 25, -8, 1

Offset: 0

Author

Wolfdieter Lang, Jul 24 2001

Keywords

• sign
• easy
• tabf

Comments

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).

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.

Row sums N6(n,1)=1 for all n.

Examples

			{1}; {1}; {1}; {1}; {1}; {1}; {5, -10, 10, -5, 1}; {4, -5, 0, 5, -4, 1}; ...
c=2: b(2,1)=b(2,2)=1, b(2,j)=0 for j=3,4,5.
N6(7,x)=4-5*x+0*x^2+5*x^3-4*x^4+x^5.
		

Formula

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).