|
Search: id:A002195
|
|
|
| A002195 |
|
Numerators of coefficients for numerical integration.
(Formerly M4809 N2056)
|
|
+0
7
|
|
| 1, -1, 11, -191, 2497, -14797, 92427157, -36740617, 61430943169, -23133945892303, 16399688681447, -3098811853954483, 312017413700271173731, -69213549869569446541, 53903636903066465730877, -522273861988577772410712439, 644962185719868974672135609261
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
H. E. Salzer, Coefficients for numerical integration with central differences, Phil. Mag., 35 (1944), 262-264.
H. E. Salzer, Coefficients for repeated integration with central differences, Journal of Mathematics and Physics, 28 (1949), 54-61.
T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 545.
|
|
FORMULA
|
a(n)=numerator of (2/(2*n+1)!)*int(t*product(t^2-k^2, k=1..s), t=0..1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
|
|
EXAMPLE
|
a(1)=-1 because (1/3)*int(t*(t^2-1^2),t=0..1)=-1/12.
|
|
MAPLE
|
a:=n->numer((2/(2*n+1)!)*int(t*product(t^2-k^2, k=1..n), t=0..1)): seq(a(n), n=0..16); (Deutsch)
|
|
CROSSREFS
|
Cf. A002196.
Adjacent sequences: A002192 A002193 A002194 this_sequence A002196 A002197 A002198
Sequence in context: A034787 A001408 A036936 this_sequence A068649 A072290 A112127
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
|
|
|
Search completed in 0.002 seconds
|
