|
Search: id:A093557
|
|
|
| A093557 |
|
Triangle of denominators of coefficients of Faulhaber polynomials in Knuth's version. |
|
+0
4
|
|
| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 6, 15, 3, 15, 30, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 2, 1, 1, 5, 2, 5, 10, 1, 1, 3, 2, 7, 1, 3, 42, 21, 21, 1, 1, 2, 3, 2, 1, 6, 15, 3, 5, 10, 1, 1, 1, 5, 3, 10, 5, 15, 5, 5, 1, 1, 1, 1, 6, 3, 2, 3, 3, 7, 1, 1, 14, 21, 42, 1, 1, 1, 2, 1, 1, 1, 1, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
The companion triangle with the numerators is A093556, where more information can be found.
|
|
LINKS
|
W. Lang, First 10 rows.
|
|
FORMULA
|
a(m, k)= denominator(A(m, k)) with recursion: A(m, 0)=1, A(m, k)=-(sum(binomial(m-j, 2*k+1-2*j)*A(m, j), j=0..k-1))/(m-k) if 0<= k <= m-1, else 0. From the 1993 Knuth reference, given in A093556, p. 288, eq.(*) with A^{(m)}_k = A(m, k).
|
|
EXAMPLE
|
[1]; [1,1]; [1,2,1]; [1,3,3,1]; ...
Denominators of [1]; [1,0]; [1,-1/2,0]; [1,-4/3,2/3,0]; ... (see W. Lang link in A093556.)
|
|
CROSSREFS
|
Sequence in context: A117185 A129181 A157694 this_sequence A098802 A048804 A158565
Adjacent sequences: A093554 A093555 A093556 this_sequence A093558 A093559 A093560
|
|
KEYWORD
|
nonn,frac,tabl,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 02 2004
|
|
|
Search completed in 0.002 seconds
|
