|
| |
|
|
A094075
|
|
Denominator of I(n)=integral_{x=0 to 1/n}(x^2-1)^3 dx.
|
|
0
|
|
|
|
105, 13440, 229635, 1720320, 8203125, 29393280, 86472015, 220200960, 502211745, 1050000000, 2046152955, 3762339840, 6588594285, 11068417920, 17940234375, 28185722880, 43085560665, 64283103360, 93856532595, 134400000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The numerator is b(n)=-105*n^6+105*n4-63*n^2+15. E.g. b(3)=-68392.
|
|
|
LINKS
|
Table of n, a(n) for n=1..20.
|
|
|
FORMULA
|
a(n)=105*n^7=105*A001015.
G.f.: 105*x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^8 [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
|
|
|
EXAMPLE
|
E.g. I(3)= -68592/229635.
|
|
|
MATHEMATICA
|
f[n_] := Integrate[(x^2 - 1)^3, {x, 0, 1/n}]; Table[(-105n^6 + 105n^4 - 63n^2 + 15)/f[n], {n, 20}] (from Robert G. Wilson v May 03 2004)
|
|
|
CROSSREFS
|
Sequence in context: A075914 A075924 A199353 * A018233 A199519 A082368
Adjacent sequences: A094072 A094073 A094074 * A094076 A094077 A094078
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Al Hakanson (hawkuu(AT)excite.com), Apr 29 2004
|
|
|
EXTENSIONS
|
G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
More terms from Robert G. Wilson v, May 3 2004
|
|
|
STATUS
|
approved
|
| |
|
|
