|
Search: id:A128064
|
|
|
| A128064 |
|
A natural number transform. |
|
+0
23
|
|
| 1, -1, 2, 0, -2, 3, 0, 0, -3, 4, 0, 0, 0, -4, 5, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 0, -7, 8
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
The matrix inverse = (1/1; 1/2, 1/2; 1/3, 1/3, 1/3;...). Binomial transform of A128064 = A128065 A128064 * A007318 = A103406
The positive version with row sums 2n+1 is given by T(n,k)=sum{j=k..n, C(n,j)*C(j,k)*(-1)^(n-j)*(j+1)}. - Paul Barry (pbarry(AT)wit.ie), May 26 2007
Binomial transform of unsigned sequence is A003506. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2007
|
|
FORMULA
|
Triangle read by rows: row 1 = 1, row 2 = (-1, 2); (n-2) zeros followed by -(n-1), n. Infinite lower triangular matrix with (1, 2, 3,...) as the right border, (-1, -2, -3,...) as the adjacent diagonal and the rest zeros.
Number triangle T(n,k)=sum{j=k..n, C(n,j)*C(j,k)*(-1)^(j-k)*(j+1)} - Paul Barry (pbarry(AT)wit.ie), May 26 2007
|
|
EXAMPLE
|
First few rows of the triangle are:
1;
-1, 2;
0, -2, 3;
0, 0, -3, 4;
0, 0, 0, -4, 5;
...
|
|
CROSSREFS
|
Cf. A128065, A103406.
Cf. A003506.
Sequence in context: A053571 A129883 A098489 this_sequence A144217 A132814 A058623
Adjacent sequences: A128061 A128062 A128063 this_sequence A128065 A128066 A128067
|
|
KEYWORD
|
tabl,sign
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 14 2007
|
|
|
Search completed in 0.002 seconds
|
