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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
OFFSET
1,1
COMMENTS
The numerator is b(n) = -105*n^6+105*n4-63*n^2+15. E.g., b(3) = -68392.
FORMULA
a(n) = 105*n^7 = 105*A001015(n).
G.f.: 105*x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^8. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
EXAMPLE
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}] (* Robert G. Wilson v, May 03 2004 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {105, 13440, 229635, 1720320, 8203125, 29393280, 86472015, 220200960}, 20] (* Harvey P. Dale, Aug 04 2023 *)
CROSSREFS
Sequence in context: A263888 A269474 A255497 * A199519 A082368 A001546
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)excite.com), Apr 29 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 03 2004
G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009
STATUS
approved