|
Search: id:A093559
|
|
|
| A093559 |
|
Triangle of denominators of coefficients of Faulhaber polynomials used for sums of even powers. |
|
+0
3
|
|
| 6, 10, 30, 14, 14, 42, 18, 9, 10, 30, 22, 33, 66, 22, 66, 26, 26, 78, 273, 910, 2730, 30, 30, 15, 9, 90, 2, 6, 34, 51, 51, 51, 102, 51, 170, 510, 38, 19, 95, 95, 190, 57, 3990, 266, 798, 42, 14, 7, 21, 6, 66, 1386, 693, 110, 330, 46, 138, 46, 23, 230, 690, 345, 23, 230, 46
(list; table; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
The companion triangle with the numerators is A093558. See comment there.
|
|
REFERENCES
|
D. E. Knuth, Johann Faulhaber and sums of powers, Maths. of Computation 61, 203 (1993) 277-294.
Ivo Schneider, Johannes Faulhaber 1580-1635, Birkhaeuser Verlag, Basel,Boston,Berlin, 1993, ch.7, p. 131-159.
|
|
FORMULA
|
a(n, m)= denominator(Fe(m, k), with Fe(m, k):=(m-k)*A(m, k)/(2*m*(2*m-1)) with Faulhaber numbers A(m, k):=A093556(m, k)/A093557(m, k) in Knuth's version. From the bottom of p. 288 of the 1993 Knuth reference.
|
|
EXAMPLE
|
[6]; [10,30]; [14,14,42]; [18,9,10,30]; ...
Denominators of [1/6]; [1/10,-1/30]; [1/14,-1/14,1/42]; [1/18,-1/9,1/10,-1/30]; ...(see W. Lang link in A093558.)
|
|
CROSSREFS
|
Sequence in context: A097578 A103767 A025129 this_sequence A130440 A137272 A121801
Adjacent sequences: A093556 A093557 A093558 this_sequence A093560 A093561 A093562
|
|
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
|
