A063266 Coefficient array for certain numerator polynomials N7(n,x), n >= 0 (rising powers of x).

1, 1, 1, 1, 1, 1, 1, 6, -15, 20, -15, 6, -1, 5, -9, 5, 5, -9, 5, -1, 4, -3, -10, 25, -24, 11, -2, 3, 3, -25, 45, -39, 17, -3, 2, 9, -40, 65, -54, 23, -4, 1, 15, -55, 85, -69, 29, -5, 21, -70, 105, -84, 35, -6, 15, -19, -95, 396, -751, 917, -792, 495, -220

Offset

0,8

Comments

The g.f. of column k of array A063265(n,k) is (x^(ceiling(k/6)))*N7(k,x)/(1-x)^(k+1).

The degree sequence for the polynomials N7(n,x) is [0,0,0,0,0,0,0,5,6,6,6,6,6,5,11,...].

All row sums N7(n,1)= 1.

Links

Table of n, a(n) for n=0..62.

Formula

a(n, m)=[x^m]N7(n, x), n, m >= 0, with N7(n, x) = sum(((1-x)^(j-1))*(x^(b(c(n), j)))*N7(n-j, x), j=1..6), N7(n, x)= 1 for n=0..6 and b(c(n), j) := 1 if 1<= j <= c(n) else 0, with c(n) := 5 if mod(n, 6)=0 and c(n) := mod(n, 6)-1 else; hence b(0, j)=0, j=1..6.

Example

{1}; {1}; {1}; {1}; {1}; {1}; {1}; {6, -15, 20, -15, 6, -1}; {5, -9, 5, 5, -9, 5, -1}; ...
c=3: b(3,1)=b(3,2)=b(3,3)=1, b(3,j)=0 for j=4,5,6.
N7(8,x)= 5-9*x+5*x^2+5*x^3-9*x^4+5*x^5-x^6.

Crossrefs

Sequence in context: A277951 A176849 A087110 * A131892 A291381 A280719

Adjacent sequences: A063263 A063264 A063265 * A063267 A063268 A063269

Keyword

sign,easy,tabf

Author

Wolfdieter Lang, Jul 24 2001

Status

approved