|
| |
|
|
A091917
|
|
Coefficient array of polynomials (z-1)^n-1.
|
|
2
| |
|
|
1, -2, 1, 0, -2, 1, -2, 3, -3, 1, 0, -4, 6, -4, 1, -2, 5, -10, 10, -5, 1, 0, -6, 15, -20, 15, -6, 1, -2, 7, -21, 35, -35, 21, -7, 1, 0, -8, 28, -56, 70, -56, 28, -8, 1, -2, 9, -36, 84, -126, 126, -84, 36, -9, 1, 0, -10, 45, -120, 210, -252, 210, -120, 45, -10, 1, -2, 11, -55, 165, -330, 462, -462, 330, -165
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| The first element has been changed to 1 to produce an invertible matrix. Alternatively, this is the coefficient array for the polynomials P(z,n)= product{j=0..n-1, z-(1+w(n)^j)} where w(n)=e^(2pi*i/n), i=sqrt(-1).
The row entries determine interesting recurrences. For instance, a(n)=4a(n-1)+6a(n-2)+4a(n-3), a(0)=a(1)=a(2)=1, gives A038503. Sequences of the form a(n)=sum{k=0..n, if (mod(k,m)=r, binomial(n,k), 0)}, for r=0..m-1, result. Equivalently, a(n)=sum{j=0..n-1, 2^n(cos(pi*j/m))^n*cos((n-2r)pi*j/m)}/m, r=0..m-1. These include A024493, A024494, A024495, A038503, A038504, A038505. The inverse matrix is A091918.
Triangle T(n,k), 0<=k<=n, read by rows given by [ -2, 2, 1/2, -1/2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 11 2007
|
|
|
EXAMPLE
| Rows begin {1}, {-2,1}, {0,-2,1}, {-2, 3, -3, 1}, {0,-4, 6, -4, 1},...
|
|
|
CROSSREFS
| Sequence in context: A035443 A180430 A036261 * A025657 A025686 A022329
Adjacent sequences: A091914 A091915 A091916 * A091918 A091919 A091920
|
|
|
KEYWORD
| sign,tabl
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 13 2004
|
| |
|
|
